No, followers do not wear out weapons from normal use like the player. What you are seeing is the enemies hitting the weapon itself. A sniper rifle has a
HUGE model making it easy to for an enemy to hit. With 80 item hit points it takes very few of these hits to break the weapon.
Give Boone the All-American and some 5.56mm surplus ammo. Better yet a Brush Gun with some SWC ammo. It'll be very obvious very quickly there is no weapon degradation from use in this case.