can a non powered tribble breed and produce a tribble that has a power?
No, mutant tribbles don't have the right to marry. Yet.
Actually, I think we can beat the EVE players here. BoB was infiltrated by Goonsquad and destroyed from within--guild espionage writ large. I will join the premier Klingon PVP fleet with a human disguised as a Klingon, then throw a roast beef sandwich along with a tribble into their bank. Even better espionage!