Plenty of them split to Canada for the duration of Vietnam. I think Carter eventually pardoned them.
I once knew a man much, much older then me who was born in Italy but brought to US in his infancy long before WW2. He was actually drafted by Mussolini but ignored it. Probably in the late 1960’s he wanted to visit his home country for the first time but found out he still had an outstanding Italian warrant for his arrest. Got it fixed okay.
If by "duration" you mean post 68, yes. Before that, not so much.