Of course. The class ship doesn't have to be in active use, but it still has to have existed at some point, even if it was only a prototype.
IMHO, I actually like the thought that the Constitution was in active service. It helps to propound the thought that there was nothing inherently special about the Enterprise - that it was just another ship of its class. Of course the Enterprise had an exceptional crew, nobody's denying that, but the actual SHIP was just one of many. I think that was the intention after all.
Besides, the class was - out-of-universe - named after the real life USS Constitution, 'Old Ironsides', so I'm sure the Trek version was an important, active ship as well.
I personally would also prefer the USS Constitution NCC-1700 (?) be an active ship, in the same way the USS Excelsior was for the Excelsior class, and the USS Galaxy was for the Galaxy class ships. I was just saying that it's possible to have had the Constitution as a test ship, that wasn't on regular deployment. But even as a test bed ship, it still is important.