From what I can tell, in the early days, what region of Italy a guy's ancestors came from may have held some weight. That's when the rivalries between Sicilian, Neapolitin, Calabrian, etc. were more apparent. But fast forward a few generations, when Italians have become assimilated in the mainstream American culture, as well one type of Italian marrying another type of Italian, and I don't think it matters anymore. If a guy is well connected enough, a good earner, etc. he stands a good chance of getting made as long as his last name is of Italian descent - hence him having some Italian blood.

The point being, if somebody is of Arbereshe descent, he probably also has some Italian blood along the way as well so it probably wouldn't make much difference as long as the other criteria above are met.