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.
Or that is the norm? First ship is 2000 and that doesn't change and she's the first ship. First ship is 1700 and she's still the first ship. We're not given any indication that the Excelsior had an unusual naming convention or classification.
Oh, absolutely. There is nothing on screen to indicate any rhyme or reason to the registry numbers on starships. I was just pointing out how Jefferies' 17th ship design, 1st build template could be used despite there being an NCC-1700, which doesn't seem to fit. It makes just as much sense to have NCC-1700 be the first ship of the series, or have the first ship of the series/class be NCC-1681 for that matter. Nothing on screen says that Star Ship/Constitution/Enterprise have to have registries that start with NCC-17xx.
"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