There's stories about Sam Giancana getting Sinatra lucrative movie parts when his career was flagging.

He was questioned by authorities in 1951 over a suspicion that he had transported money for the mob to Havana. He was hired to provide the entertainment at a summit of mobsters including the exiled Lucky Luciano.

I think Frank definitely liked to keep company with wiseguys and they liked him, he was a source of pride for Italian Americans.