It wouldn't have been the Mafia that killed Thomas Dewey, it would have been Dutch Schultz, a non-Italian bootlegger who Dewey prosecuted. Schultz wanted to kill Dewey, and was planning to do so, when the Mafia had him killed, to prevent him from killing Dewey, and to take out a major non-Italian crime kingpin. He did convict "Lucky" Luciano, but even then Luciano just moved his operations to Cuba, rather than going back to Sicily.
If Dewey is killed by Schultz, then this is going to bring all kinds of heat. The hunt against La Cosa Nostra might start very early, and could make for some interesting politics during WWII, if the Mafia helped the Allies in Sicily as much as some histories would have us believe.