Here's what you're trading for the alertness feat if you don't take the abil score upgrade and instead take the feat:
- +1 to damage
- +1 to hit
- +1 to AC
- +1 to Dex saves
- +1 to Dex checks
- +1 to init
The question then, ultimately, becomes, is +5 init (net +4), no surprise and no advantage on attacks against from hidden opponents worth it.
The latter two features are very dependent on your campaign and DM. Surprise should be a fairly frequent occurrence on both sides of combat, but that still depends on how willing your DM is to allow it or stage his monsters to have them obtain it (and kind of how cautious your group tends to be). Monsters attacking from hidden is another one that really depends on your DM, you group and how well you guys are at nosing out monsters from the shadows.
So ignoring those two items since they are DM and campaign dependent (and thus can't be weighted objectively), the question then becomes, is +1 to Dex more or less beneficial over 4 levels than +5 to init.
For pretty much any character other than the Assassin Rogue, I'd probably argue that they should take the stat upgrade early, the feat at L8 and then the last stat upgrade. However +5 init has amazing synergy with the Assassin Rogue and you're going to get a ton of mileage out of it.
If you're already at 20 Dex (if you managed to start at 20, or 18 and are at L8), then there really isn't any stat upgrade that is worth taking over this feat (though there may be better feats). Rogues are skill monkeys, yes, but +5% in a single ability set of skills is not worth the +25% to initiative and other features o this feat. The only one that would be worth considering at all is Con for the extra HP, but it's really not that many and you're better of boosting your damage significantly.
Take the feat at L4 (or even better, play a human and take it at L1).
There is nothing in Alert that prevents you from being pickpocketed.
Surprised is a very specific state which refers to the beginning of a combat. Surprise is a state where a creature is unaware of another creature when combat begins, in this case the surprised creature a) cannot take an action on its first turn and b) cannot take reactions until after its first turn.
It has nothing to do with out of combat situations such as being pickpockted.
Best Answer
From the section on Surprise, PHB 189:
What the Alert feat does is it allows you to take your normal set of actions during the first round of combat, despite surprise. It doesn't let you see your foes automatically, it just lets you know that there are foes to be seen.
What this means is that you have a chance to do something at the same time as your enemies. You could dive for cover, or cast a spell, or possibly make an active Perception check to spot your enemies and attack.
In your example, when the hidden enemies roll for initiative and start firing, the Alert character knows that they are under attack fast enough that they can (if their initiative is high enough) jump out of the way or cast a defensive spell, reducing the effect of the ambush. Since surprise is determined on a personal level, and not a party level, only the Alert character gets these benefits, not any of their party members.