If you believe Jeff Chandler is Italian, they I can probably pass for an Eskimo. Putting that disbelief aside, Chandler does a decent job of portraying a racketeer that has been deported.
In reality, the Justice Department seldom deported small-time crooks who just took care of the rackets in various towns; they deported killers they could not get a conviction on because all evidence was wiped out. Guys like Lucky Luciano and the like were far more likely candidates for deportation.
In any event, the story is entertaining, and the subplot of the romance with an Italian countess is interesting. The local hoods, however, in these small Italian towns, are really more like small-time crooks, rather than extremely dangerous criminals. The Hollywood theme of the hood who turns good, is highly unlikely, but entertaining.
The end result is that Chandler pretty much gets to do whatever he wants, but this could never happen in a major Italian city.