Definitely, I like your idea, and maybe a very small chance to permanently increase the associated stat; though the increase would have to be minimal. And maybe a cooldown on it, maybe not based on the likelihood of the increase. Though, that might also be a terrible idea. Or maybe separate evolution paths, where the more difficult one to obtain could permanently boost (still with the miniscule chance of a permanent increase), but the other would give bigger boosts (temporary though).
I don't really know the stat system very well, but at least I know that such a creature would have to be