It's possible to perpetrate a good deed, but not likely. That's because perpetrate means to commit or be responsible for something — usually something mischievous or bad.
If you manage to slip a whoopee cushion under your teacher's rear without her seeing it, then you've perpetrated a classic prank. But if you use your wily ways to break into the bank's safe, then you've just turned yourself into "a felony-class perpetrator." So do yourself a favor and stick to perpetrating lesser crimes.