Re: USS Copernicus, NCC-640 or 623?
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
Well, that's just speculation. We don't really know what an "atomic pile reactor" is or what it does, and we don't even know if the Enterprise had one too or not. As you said, it really doesn't help, unless someone stated that said device was only used on ships older than the Constitution class.
“Don’t believe everything you read on the internet.”
– Benjamin Franklin