I don't think Ciccio would have follwed him there. But then again, would he even know where he went. All he knows is that he ran away-he could have moved over to the next town, to Rome, or to London, England. Ciccio was not going to have every Andolini in New York City killed because of a hunch.
But then again, do you think that Vito would have ever been able to set up a meeting with Ciccio to take his revenge if his name was Andolini?