Does Elite Coil +Explosion / impact damage affect other weapon damage?

[Quasinerdo]

Elite coils.
Some have a status effect of "X% extra damage from explosion or impact damage while in this state"

Does this effect work with damage from weapons other than the one with the coil?

Eg: I hit with bow that has Elite Fire Coil and put machine into burning state.

Will hits from my Forgefall Sharpshot bow with impact ammo gain the x% extra on top of any other burning bonuses?