They were on the losing side.
Obviously, they, themselves, started out as a wandering band of Celts, Troy, or Illium (or in other Celtic languages Allium) being a Celtic site.
So, early Celts in Italy planted grapes.
No Italian who knows his classical history would have a problem with that.
Seems unlikely, since if the Trojan War took place it was about a thousand years before the Celts showed up in the area of Greece/Asia Minor.
I would! It was Lucy! I have pictures!
Actually, only the Romans did.
Prior to the Social War (also called the Italian War or the Marsic War) an "Italian" would have been considered a citizen of one of the non-Roman city states on the Italian peninsula allied to Rome.
Denarius of the Marsian Confederation, during the Social War (89 BC). The legend "Italia" is in Oscan.
As for northern Italy, Cisalpine Gaul was a Celtic area prior to and after the Roman conquest (thus its name) and modern day northern Italians would therefore have no problem acknowledging their direct Celtic ancestors.
What have we lost from the Carthaginians aka Phoenicians?