Virgin USA (or whatever it will be called) is nothing to do with Virgin Atlantic, and will have no staff in common - just like Virgin Blue and Virgin Express (though Blue and Atlantic have a small cabin-crew exchange program). The philosphies and procedures of lo-cost shorthaul and premium-service longhaul are pretty incompatible.
The airline ownership rules in the USA are under discussion at the moment, and may allow a greater percentage of foreign ownership before long. That said, it seems certain that the Virgin USA airline will be majority US-owned (though some of the shareholders may themselves be part owned by Virgin....!). The flight deck staff will have to be FAA-licenced (the aircraft will have to be N-reg), but there may well be some green-card-holding Brits elsewhere in the airline.