Star Trek: Enterprise?

In Star Trek: First Contact, if the Enterprise-E and the fleet had destroyed the Borg ship before it went back in time to sabotage Zefram Cochrane and The Phoenix, would the NX-01 Enterprise and the events of Star Trek: Enterprise have still occurred? Under those cirstances, what would happen if someone asked James T. Kirk if he'd ever heard of Jonathan Archer and the NX-01 Enterprise?