...and there was definitely a Constitution...at Wolf 359.
I wonder, would any of the ships that fought at Wolf 359 be using the TOS Movie-era lifeboats shown in Mr. Scott's Guide To The Enterprise? It seems there was at least 1 Constitution-class ship in that batter, after all.
Not to be needlessly nitpicky, but there's no direct evidence that a Connie was at Wolf 359. All we see is part of a saucer in one scene, and part of a secondary hull in another scene. There's no indication that they were part of the same ship, or that the ship those hulls came from was a Constitution (i.e. another class of ship could have had an identical secondary hull, etc.)
Now speaking real-world, that's exactly what they were, because that saucer and secondary hull was from the destroyed Enterprise from STIII. The saucer was used again for the U.S.S. Olympia, but again that doesn't mean the Olympia was a Constitution either.