Fat Princess is the only character that is from a PSN game (the only one I can think of). Imagine if the PS3 was like the PSOne and PS2 and had no PSN. Fat Princess might not have been made. Would this game really be different if there wasn't a Fat Princess running around for cake?
Solely for the fact that almost no one uses her, I'm gonna have to say no.
Fat PRincess was around since the beta. If she wasn't there, there could've been an extra slot.