Yes, during the 1910's and 1920's it became more of a Chicago thing and later it was renamed as the Italo-American union.

Btw, did you guys ever heard of the Italian society from 1870's/80's known as Unione e Fratellanza in Chicago and NY? Well I personally believe that was the real "predecessor" of the Unione Siciliani and allegedly was completely legitimate, but as any other civil organization, it is quite possible there were already some criminal donators within the organization, probably disguised as legitimate businessman.