I don't think this character will be overpowered. In fact, I suspect that the other characters will be underpowered — the math of D&D 4E is engineered for characters who have at least a 16 in the score most related to their class: Strength for fighters, for example.
As for the question of whether this character will be a "Mary Sue," the question is difficult to answer in terms of roleplaying games — characters in RPGs often are hypercompetent and well-loved by the populace, even those hard to convince. It's the portrayal, not the mechanics, that determines Mary or Marty.
Erik Schmidt's answer is probably the better one to go with (as it'll help you find the root cause), but I'll contribute a bit based on what I see from your description.
From your description, you have a player who enjoys:
And who doesn't enjoy:
And yet, this player is playing in a campaign that is low combat, high intrigue, and where the penalties for building a new character are incredibly prohibitive.
When players are marginalized, they tend to try to get into the spotlight in any way that they can. And that leads to disruptive behavior.
This leaves you with a few choices:
Try to get the player into a campaign that they'd enjoy (either by running an additional campaign, or by encouraging them to find/create a new group).
Remove the player from your campaign.
Find ways to compromise, attempting to bring your campaign and the problem player closer together.
The important thing to realize is that there is no way to force the player to like playing the way you and your other friends are playing.
Some people like to play the same character, and enjoy the process of growing and developing that character. Other players prefer the creation process, authoring new characters and mechanical combinations.
Dealing with the first sort of player is pretty easy. That's traditional, long-form writing. We see examples of it all the time in many different forms of fiction.
The second sort of player, the one you have now, is a bit harder to deal with. Here are a few things I've picked up to help deal with that:
Either introduce the character during downtime ("And so the party rested for six months, and met a new companion"), or use the "poof" method ("of course I've always been a catfolk fighter. Human wizard? Ridiculous."). You want to avoid having players stuck constantly in the untrustworthy rookie slot.
Maintain player parity
New characters should be (or quickly become) the equals of established characters. It's no fun being the one guy who doesn't have an artifact.
The rule of thumb is that anything that's relevant frequently, whether it's powerful mechanically or narratively. A new character can probably be allowed to do without a one-time favor from a noble. But they should probably get written into a life-debt from the king of the current kingdom (or be given something else).
If the new character doesn't start with this stuff, then the stated goal should be to catch them up quickly (within a few sessions).
A level penalty is right out, unless it's a temporary one (or you're playing a game where levels aren't super important). For example, in my 7th Sea campaign, new characters start slightly below the lowest player. But all players are brought to the same experience total periodically.
Let them know that they won't get some of the depth other characters do, but make an effort anyway
From a DM's standpoint, the hardest thing about a character jumper is that you can't be sure of who they will be in the future. So if it takes you three months to author a storyline featuring that character, and they change characters every two, that creates an obvious conflict.
Let the player know about this, and give them an opportunity to work with you. And make an effort to work their current character into the plot from time to time anyway, as a show of good faith.
Combat and Intrigue
It sounds like this player enjoys combat quite a bit. Most likely, it's a chance to see how the mechanics of their character work, and to show off a little bit. This is all fine, except when it stomps all over the intrigue that other players want.
Give them combat
The easy answer here, is to make sure you're providing combat. Don't make talking the ultimate super-power. Give him a mixture of fodder that he can easily crush, and challenging mechanical opponents.
This is where the bit about parity and artifacts above becomes important. If their well-honed killing machine is constantly shown up by the senior characters with artifacts, the combat probably won't scratch their itch for them.
Signal shifts to intrigue mode
Provide clear signals to the group when a shift to intrigue mode is happening. Set intrigue in populated areas (cities, etc.) and combat outside of it. Have combat-based foes rush the group, snarling (or ambush them with a poisoned blade), while intrigue-based foes sit calmly on their thrones.
If nothing else, the occasional reminder that "Baron VonEvil is pretty well connected. Are you sure you want to fireball his face?" can help quite a bit.
Always have a backup plan
This player is going to blow stuff up. As the person who's planning things, that should be a possibility that you consider. How do you keep the plot moving if the villain doesn't get a chance to monologue? What happens if the whole room is fireballed?
The goal isn't to always have a way for the PCs to succeed per se, but simply for the story to always have a way forward. Perhaps that means that a scheme of the late baron crops up shortly after the heroes fail to find the documents, and now they have a fresh chance to investigate.
Or perhaps the important documents were partially sheltered by the lockbox they were in. They've been badly charred, but there's enough there to make out a new location to investigate. Is it a trap? Of course it's a trap. They're going in blind.
Talk to your players. Not just about how you want them to behave, but about what you're trying to do, and how you're trying to shape the campaign to the individual players. Make it a dialogue, and solicit their feedback.
I'm trying to add in some more interesting "boss fights." What did you think of that last one?
I really liked the way you guys managed to outsmart Baron VonEvil. That's given me some interesting options for the next couple of adventures.
My goal is to tell an epic story of your rise to power. I think we could use a bit more of the political stuff, I just need to work out how to write that.
There are two excellent sections in roleplaying books that I'd highly recommend for dealing with this problem, if you can get your hands on them.
The first is for the entire group. It's located in the 7th Sea Players' Guide, on page 238 under the heading Resisting the Story.
It's a couple pages long, so I won't reproduce the entire thing here. But the representative part of it is this:
Don't poison the PC pool. Don't act destructively just because "it's in your character," and don't force other players either to ignore your action or kill your character because it's in their characters. Know where the line is and make sure you -- and your Hero -- never cross it.
This doesn't mean that there shouldn't be any conflict within your party. On the contrary, some of the best and most rewarding roleplaying experiences come from moral or ethical disputes between Heroes. As long as you know where the limits are, and when engaging conflict becomes irreconcilable conflict, feel free to pursue arguments with your fellow Heroes.
The Rich Burlew essay Making the Tough Decisions is another valuable discussion of this principle.
The second is for the DM. It's located in the 4th Edition Dungeons & Dragons Dungeon Masters' Guide (pages 8 through 10). It's a breakdown of the different kinds of players, why they come to the table, and how a DM can target each one.
This is a lot of text, and only really brushes on a lot of important topics. The core assumption here is that you would rather play with this player, than necessarily play your campaign as it exists now.
The key is to give the problem player things that they enjoy. With good communication, a willingness to tune your campaign to the players, and a bit of compromise, the problem player may become a lot more tractable when their needs are met.
Are you overreacting? Yes and no.
Keep in mind that while all of you are at the same table, you are not all playing the same game. It sounds like you are a story player. All you care about is the narrative flow of the story, and what your character should logically do in that situation. Your "Problem player" is an achievement player (usually called rule lawyers, as they are more focused on the game mechanics than the narrative). He is trying to "win" at everything, and to fail when the mechanics are in their favor is like being killed by an enemy in a video game only because your hitbox is larger than your visible character. (AKA, it feels like being cheated)
How much you enjoy the game will depend on how much you can tolerate this other player playing a different game from you, so the more you tolerate it, the more you will have fun. At the same time, this behavior is disruptive and should be kept to a minimum. After all, he is not the only player, and it is important that EVERYONE have fun.
In the case about asking about HP; You are thinking "narrative, who is willing to do this?" He is thinking "Who can take this hit with the smallest chance of getting killed later because of it?" This is ok. You can mix meta-knowledge with in game decisions as long as you keep the game moving.
To flip this around, assume that a powerful entity makes you an offer you can't refuse (you can, but in character, you wouldn't want to); and as part of the deal, you have to kill the bard. So you murder the bard in his sleep. To the bard player, you are the problem player because you did "What your character would do" over what is fun for the rest of the players. (This is a bit contrived, but hopefully it illustrates what I mean about how playing in any way other than "lets all have fun" can be problematic behavior. Meta-gaming isn't the problem, it is just the form the problem has taken)
As for what you can do about it...
1) Ask yourself what the problem is.
Telling the DM that another player is meta-gaming isn't going to solve anything. The DM knows this, and everyone is doing it to some degree. If you want to fix the problem, first you need to determine why you are upset about the behavior. What part of it is making the game not fun for you? (In this common clash, it is usually because the meta-gaming slows the progression down, followed by breaking immersion by characters acting on things they don't know about)
2) Come up with solutions
The best way to get results is to suggest measurable/actionable changes that will allow all parties to still have fun. The less that actually needs to change, usually the better. You will almost inevitably need to compromise on this, but this gives you something solid to start negotiating on.
For example, you could suggest that the player can only challenge the DM x times per session/hour, or for so many minutes per hour.
3) Talk to the DM and Player
I suggest talking to the DM first, because they can help you though steps 1 and 2, and help you craft your argument for 3 to the player. The DM wants everyone to have fun, so feel free to talk to them. Let them know what you enjoyed, and what you aren't enjoying. (I recommend starting with what you are enjoying to the DM, because he is a faulty human. If you only tell him when you aren't having fun, he will think you are never having fun. Or at least doubt how much fun you are having. DMs like to be appreciated too!)
When talking to the player, don't make it immediately about them. Putting them on the defensive will make them dig in to defend themselves. Start with why YOU aren't having fun. The player can defend his own antics, but he can't refute how you personally feel when nothing progresses narratively for 30 minutes. This is where talking to the DM first shines. You want to be clear about why you aren't having fun, and work with that player to remedy it without directly attacking him. (easier said then done, but with practice comes mind control... I mean persuasion)
4a) Assuming 3 went well, and the other player actually cares how you feel
Don't let it happen in game. Telling the other player not to argue mechanics is like telling someone to stop cursing. It's habit, and the only way to break it is to address it while it is happening. If you address is after, it will have an extremely diluted effect, especially as more time passes. In general, give them 5 minutes to debate, than remind them that the story must go on! Hopefully over time the behavior will improve.
4b) Assuming 3 didn't go well, or the player is a jerk
If a player is toxic, and won't (at least try to) correct themselves, it is better to boot them from the group, than to deprive the rest of the players of their fun. Usually this should be agreed upon by everyone in the group beforehand, but sometimes this is the only feasible solution to problematic players.
0) Make sure everyone, including you, is having fun
At the end of it all, everyone is there to have fun. Everyone can be the problem player to a degree from time to time. Try to understand what others enjoy of the game so that you can help them enjoy it. And share what you enjoy so that they can help foster those elements. Forgive your fellow players every now and then, just as you will sometimes need to ask forgiveness from them. This isn't about you, or him, or the DM. It's about all of you coming together to have fun, so remember to foster that.