Nnnnnnope, Persona 1 had a girl's dream world that threatened to overwrite our reality thanks to a machine (and part of the girl's mind wanted the world to end, so...), or the Snow Queen, which, again, froze time or the world (can't remember) in the route's bad end.
And, again, I've played 1, III and IV in the mainline series. III is the exception, because the Demi-Fiend is, by definition, half-demon, so of course he gets demon powers (and even then he got those from a parasite implanted by Lucifer, not from contracting). Neither I and IV imply you get demon powers from contracting.
The best you can get is fusing with a demon, or becoming a demon yourself. Contracting doesn't give you anything other than control over the demon.