Equipment bonuses only apply where they are present. 

Let's say you send a Hero equipped with gear that increases your guardsmen's attack stats on a march. If you then send out another march led by a Captain to a different battle, the second march won't benefit from the bonus granted by the aforementioned equipment. 

Here's another example: Equipping your Hero with Crypt exploration equipment won't affect the crypt exploration efficiency of your Captains, because the gear is in the City and not actually being used by your Captains (the only units who can march to explore Crypts).