An enemy wouldn't gain any advatages for using a silenced weapon, so why should you?
Yes they could.
If an enemy were sneaking they could, say, be able to fire on you without breaking their cover and also gain a bonus to their critical rate. Depending on your PE and LK you have a chance to break their sneak, and depending on your IN and PE you have a chance to break it every time they fire (your character figures out where the bullets are coming from by mapping out angles, etc). You could bring skills into it too, obviously. Like Outdoorsman if it's in a wilderness setting, and Sneak to help to by factoring in your knowledge of hiding and cover.
You could try to get away by sneaking (Sneak, LK), run away and hope for the best (LK and AG), spray fire wildly and hope you hit them (LK, Weapon skills), hide and pray your party members can do the job (Their stats, abilities and equipment, Divine Favor), rush them with your party (Weapons, AG, LK, etc.), try intimidating them or negotiating (Your equipment, kill history, faction standings, Speech, CH, IN), hope their gun blows up (very high LK, Pariah Dog) or just die very horribly (Bloody Mess). Choices and consequences and nonlinearity and all that jazz.
This way enemies can use what you can use against them, neither side has an unfair advantage. Stats are the only determining factor, the player's sight, hearing, etc. don't enter into the equation. Just like most of us seem to want.
wasn't the Barret made in the 70's-80's?
The first Barrett was made in 1982, the first good Barrett was made in 1986. Yeah, a Barrett itself wouldn't fit the setting, but a rifle with effects analogous to it might be OK.
Its pretty much the same, weapon, the Boys just fire's a larger round.
The greater size of the round isn't enough to override the fact that the Barrett has a far higher muzzle velocity, giving it far higher penetration.
In any case, a rifle like the Barrett already exists in Fallout- the first time I saw the Bozar, I immediately thought of the Barrett. Change the Bozar's ammo type to .50 and make it a single-shot rifle and there's your Barret-alike.
The FO2 developers just copied the look of the XM109 Barrett variant (fires 25mm rounds instead of 12.7mm) and called it a Bozar. And in their slam-dump! way, decided it should be a machine gun that fires the far smaller and less powerful .223/5.56mm.
Dead ringer, huh? Just put a clip in the XM109 and flip the Bozar's bipod down.