Not really. Considering that the Intrepid-Class Intrepid would’ve only been in dry dock still being built at the time, there’s nothing to suggest that an older Excelsior or other class Intrepid couldn’t have been in service.
It would be fitting for the chief engineer of the Federation Flagship to compete with the chief engineer of the Newest Starfleet Technological Marvel. Would LaForge get so worked up about defeating an old tub?
I would assume that the whole reason why the VOY producers gave the ship's class as "Intrepid" was precisely because of that scene in TNG. And I'm not sure why there's an assumption that the prototype for the Intrepid class would be in drydock under construction. We don't know how old the Intrepid class is; we only know when the U.S.S. Voyager was commissioned. For all we know, the Intrepid could have been built during TNG's 3rd season.