So after way more consideration than this question probably deserved, here’s the synopsis.
Jonathan probably wouldn’t do too well because a proper gentleman doesn’t eat pies like a barbarian. On the other hand, he may find the challenge of a contest alluring, and therefore put his gentlemanly pride aside for a spot of fun.
Joeseph would probably go all out right from the getgo and get horrible stomach cramps, forcing him to retire early.
Jotaro would win. Don’t ask me why or how. But by the time the focus shifted to him, he’d have already put away like 10 pies.
Josuke would probably do pretty well, getting into the spirit of things and get maybe second place. Then he’d have a long talk with Okuyasu about how he retains his cool tough guy status despite losing a pie eating contest.
Giorno would start, but probably not be real into it.
Jolyne would cheat to beat Jotaro by hiding F.F under the table to help her put down but get caught and be disqualified.
Johnny will also be disqualified when his horse gets in on the action.
And Gappy got lost on his way there, resulting in a humorous, albeit creepy filler arc.
So there you have it. I’ve really scraped the bottom pits of my mind for this. I feel a piece of my soul has been lost while writing this. I need a drink.