Do weapon proficiencies carry over on dropped weapons?
Solution 1:
Yes. The proficiencies associated with the weapon picked up stay active while using the weapon. Your profile does not keep weapon proficiencies that you haven't unlocked if you toss the weapon or get killed.
It's the same as if you pick up a gun you haven't unlocked... Even though it's not available to you "in profile", you get to run around with it for a bit.