No, because that doesn't account for the redesigned NCC-1701 also being referred to as Constitution-class, starting with Roddenberry's novelization of TMP. I'm trying to be all inclusive.
Well, that's your approach, but I was addressing everyone, suggesting what, as far as I know, is a new approach, one based specifically on canon evidence. I'm asking the readers in general if they think it makes sense for two ship classes to be differentiated mainly by internal variations.
I don't think the TMP novelization is a particularly viable source, given how much about it was later contradicted even by Roddenberry himself. All the early movie novelizations take liberties; studios were a lot less strict about conformity to the finished film back then.