Joe Kennedy's involvement in liquour importing during prohibition is limited to unproven rumours. So without prohibition the Kennedys would still be as rich and influential but without people blowing unproven rumours into the cause of Joes success. After all he was an exceptional man who was well on his way before prohibition.
I think it's clear from some of the things Joe Kennedy said to the people close to him, around the time Jack and Bobby were running their hearings on organized crime, which he was deeply worried about, indicate that he had been involved with the very same gangsters at some point in his career.
Without prohibition maybe he wouldn't have made those connections, I'm sure he would have made his money elsewhere, enterprising chap that he was.
On the other hand maybe without prohibition his sons wouldn't have run those hearings at all, what with organized crime being less of a beast, and subsequently JFK's campaign for president wouldn't have been as high profile, so maybe he doesn't get elected, or maybe he has to wait another term.