If you kill people from range you are potentially missing out on XP, because:
Neutralize an enemy: 10XP
Hand-to-hand takedown: 20XP
Non-lethal: 20XP
Headshot: 10XP
So a non-lethal hand-to-hand takedown is worth 50XP, where just shooting someone is only worth 10XP (or 20XP if it was a headshot) and a lethal hand-to-hand takedown is 30XP.
However, playing non-lethal is more difficult as enemies can be revived and traq darts are slow to act (so non-lethal at range needs careful planning), and only using hand-to-hand takedowns means you're more likely to be spotted or trip an alarm.
Remember that you can get the Ghost (500XP) and Smooth Operator (250XP) bonuses for completing objectives undetected and without alarms (respectively), and I imagine they're usually worth more than the few XP lost by not taking down everyone hand-to-hand, so do whatever you need to do to avoid being detected whenever possible.
You might find What actions give XP in Deus Ex: Human Revolution? helpful.
This does mean that you aren't eligible for the Ghost experience bonus.
It does not mean that you aren't eligible for the Foxiest of the Hounds achievement.
Foxiest of the Hounds refers to if a guard runs up to an alarm panel and activates it, or a camera sets off an alarm, not the "alarmed" state that guards can go into.
Also, you already lost the "Ghost" bonus because someone spotted a body.
EDIT:
Alarmed occurs whenever a guard sees (or hears) something out of the ordinary. For example, a door open, a dead body, a hole in the wall that you punched out etc. This state varies. This state WILL disqualify you from receiving Ghost if someone spotted you or a body or something similar. This state WILL NOT disqualify you from receiving Ghost if someone spots a door opening, a hole in the wall or something similar. (At least I think this is how it works, I've received and not received Ghost in these ways, but I'm not 100% sure if this is exactly how it works)
Suspicious occurs whenever you're spotted by a camera or after guards have been hostile for a while and you've remained hidden for a while, they'll revert back to alarmed, and then suspicious. This state WILL NOT disqualify you from getting Ghost.
Hostile means that they're actively searching for your last seen location and occurs only if you've been spotted by a camera (for long enough) a robot or a guard. This state WILL disqualify you from getting Ghost.
Best Answer
It depends.
It makes the game harder because you'll be paying attention all the time to everything so that you won't be forced to start again a specific section. You'll save often.
The Pacifist run will make the game about 20% harder, because you'll be forced to use the stun gun that has a limited range and the tranquillizer gun that requires a bit of planning comparing it to the sniper.
You'll stock on non lethal weapons and focus on punchy-sleepy takedowns.
The Deus Ex Machina difficulty level won't change much considering the above statements. Enemies will kill you faster because of their increased damage, but if you're going for the The Foxiest of Hounds achievement you won't really care that much, you're sneaking and won't be in a situation for the enemies to fire at you after being detected (you'll quick load anyways when that happens).
The boss fights are the only thing to consider, but you can definitely kill them easy if you're stocking in stun gun ammo, have a fully upgraded lethal weapon and/or tyhoon ammo (2-3 blasts per enemy and they're gone). In the Director's Cut version, boss fights were re-thinked and as far as I know, you can now use Hacking to turn turrets/robots on them.
In conclusion, this could be the best to play the game. You'll be fully aware and the game will be moderately challenging.
Follow this as a guide to check if you won't miss any Smooth Operator bonuses: http://deusex.wikia.com/wiki/Foxiest_of_the_Hounds