Had Capone stayed, he definitely would not have rose as fast as he did in Chicago. Remember that in the 1920's, you still had to be full bloodied Sicilian in order to join any New York Mafia family. Capone was a Neapolitan descendant, so he wouldn't have been qualified to join (at least until they loosened the rules). I read somewhere that there were Cammora offshoots in New York at the time. But those groups are more linked by blood so unless Capone was related to someone in there, he probably was barred from joining them too.