Yes, unless it states "If ____ is the active Pokemon" or something to that effect.
And the difference between Powers and bodies is that Pokepowers happen when you activate them, eg. "Ok, I will use Claydol's cosmic power Pokepower".
Pokebodies on the other hand are always on, for example Mantine MT's Pokebody stating that while Mantine is in play all water Pokemon have 2 less retreat cost.
Hope that helps.