Do weapon precision upgrades improve your squad mates?
Solution 1:
The more precision a squad mate has, the less spreading for the shots he fires. It works in the same way that different weapons do.
If you equip your squad mate with two different sniper rifles with a significant different on the precision you can see how the shots of one of the weapon miss more often, specially on the far shots.
You can imagine it as a circle. The more precision, the smaller the circle goes, and all the shots are set in a random place on the circle when aiming for an objetive.
So yes, the weapon upgrades will work for your teammates.