In the few shots of the player using vats against humanoid npcs, the weapon the enemies were carrying didn't appear to light up and become targetable. So unless there's a perk later on that changes that, which there very well could be and would easily render my whole point moot, I don't think weapons can degrade.
It looks like armor pieces can get shot off and power armor will need repair, but as far as weapons go I haven't seen anything to hint at it still being ingame. Personally I'd rather see ammo take over the condition mantle instead of the weapons myself. I think it could create a more entertaining system to play with.