It's possible. Then again we do have NCC-2000 USS Excelsior. The lead ship of the Excelsior Class, IIRC.
Which started out as a testbed/prototype for a new class of ship equipped with "TransWarp" drive. I don't think its ever been said on screen, but its been speculated that her original registry - NX-2000 - was an indication of her eXperimental status. NCC-1700 could have initially been NX-1700 and was later commissioned as NCC-1700 after NCC-1701 had been launched.
Sure, but being the experimental ship didn't change the Excelsior from being the lead ship and having the class name. The existence of NX/NCC-1700 would've made that ship the lead ship making 1701 the second ship.
I see the chain of events like this:
- NX-1700 prototype 17th starship design built and used for trial runs.
- Trials are finished and construction begins on the 17th design's first production build: NCC-1701.
- USS Enterprise NCC-1701 is launched and commissioned.
- Sometime later NX-1700 is refitted for active service as NCC-1700
I think the class name could go either way. I wasn't really arguing either way for what class 1701 was, but rather just that she could still be the 1st build of the 17th design even if NCC-1700 exists. In the case of Excelsior, for whatever reason, they decided to convert the prototype to an active duty ship before building NCC-2001, which makes her number not technically correct, but these things happen sometimes in real life.
"Canon is only important to certain people because they have to cling to their knowledge of the minutiae. Open your mind! Be a Star Trek fan and open your mind and say, 'Where does Star Trek want to take me now'." - Leonard Nimoy