With all the kit-bashes they had in TNG it could very well be a random class that has the same secondary hull design as the Constitution refit. I mean bits from the Miranda class and Excelsior class seem to get put together like Frankensteins monster enough, the Connie obviously has too.
As for if it is a Connie refit... I believe the Ent-A became a museum piece (can't remember where I heard that, could be from a book in which case not canon), I'm pretty sure Connie's were retired at the start of the 24th century, they could have dragged one out of mothballs, in which case, there is a chance it's the Ent-A, but could well be any other Connie that got retired rather than destroyed. There's nothing on screen to suggest it either way.