Well, maybe. Evidence that the dig is actually at the site of the early Davidic dynasty is argued by many. There is even a question of whether David existed, though there is good evidence that there were Davidic kings as described in the Tanach.
As for Zionism beginning there??? How can that be? Whatever else he may have been, David was not a good man. He took the throne by violence. Jerusalem was a Canaani city with ots o0wn people, the Jebusites. Not the best image for a root of Zionism.