Not on a professional level, he was 13 when he started playing for Parma... Saying Rossi played in the U.S. is like saying that Messi played in Argentina. It was ages ago.
I do get, i made my remark about the Scots, Irish and Brits which came up as a sidecomment. In our continent bloodlines mean little, that's why exactly the US have profited from the Serbs, Greek, Ghanian, and whatever else wound up there playing for them. Mind, though that in many cases they are second-third generation Greek/Serb/whatever. Rossi probably felt more Italian than U.S.American, he moved to Italy when he was 13, then to England when he was 17. I wouldn't ever believe he feels more drawn to the U.S. than to Italy.
And last, but not least. I'd love to see both Giovinco and Rossi playing together. They do well with the Azzurrini, I am sure they could do well for Juve for many years to come.