Love the three-nacelled starship.
I don't think what we know of the ship's engineering helps us to know if the ship was older. We know that the ship had an atomic pile reactor. There was a real world analogy for this: the Chicago Pile-1. If we applied this analogy to this ship, we would have a starship powered by fission power. Do we have evidence that the Enterprise
and her sister ships had another kind of reactor?
Article on Chicago Pile-1: http://en.wikipedia.org/wiki/Chicago_Pile-1