Since Star Trek: Countdown to Darkness established that
, does that mean that Kirk's Enterprise is the "Enterprise-A"? I mean it's registry is still NCC-1701, but maybe it's official designation is the NCC-1701(a) on paper?
Actually, unless I really missed something, April's Enterprise appears only in the flashbacks of Countdown 2 and we never see its registry number.
So it can easily be assumed that it didn't have the 1701. Kirk's is the first 1701.