I wouldn’t say likely, but it is certainly possible. The Chicago machine was still a thing back then.

Joseph Kennedy was a bank owner (at least part owner) before WW I, and made a further pile in the stock market--getting out before the crash--and some I guess in movies. He bought up a bunch of distilleries, and he had booze stored under bond, but the notion that he was a bootlegger is wrong.

Was he more scrupulous than the next businessman? Maybe not. Was he in bed with the mob? I doubt it.

Mobs have attempted to rig elections, but not I think The Mob. The most conspicuously rigged election in US history must have been Hayes over Tilden, at a time when organized crime was pretty small beans in the US.