I would assume so, seeing as other stat copying moves like psych up remain in effect when the opponent switches out (at least I'm pretty sure of that), naturally though, the pokemon that switches out will have their stat boosts/lowerings reset.
I can imagine how nice a combo this will make with moves like Psychoboost and Overheat. Use the attack a couple times, Power Swap, be refreshed while lowering opponent's Special Attack or Attack, repeat on next pokemon.