In-universe, yes, it's likely that he is referring to the Enterprise E. The Enterprise D was destroyed in 2371, the E was launched in 2372 (on stardate 49827.5) and this episode took place in 2373 (stardate never mentioned in the episode, but "Looking for par'Mach in All the Wrong Places", several episodes earlier that season, mentioned stardate 50061.2).
In fact, it seems like such an obvious reference that the trivia section of the Memory-Alpha article on this episode states it matter-of-factly without citation:
This episode also contains the first reference to the new Sovereign-class USS Enterprise-E, as the film Star Trek: First Contact hadn't premiered yet. After Sisko mentions the USS Defiant was in front of the Enterprise, Dulmur tells him to be more specific, as there had been five. Lucsly corrects him and says there had been six. (The NX-01 was never in Federation service, and Star Trek: Enterprise didn't exist as a series until 2001, five years after this episode was released.)
This episode takes place months before the Battle of Sector 001 (stardate 50893.5, which matches up with the last few episodes of season 5), which means that the Enterprise likely was still undergoing shakedown or was on one of its very first missions. Memory Beta lists some books that take place between the E's launch and First Contact.
An interesting aside: the first teaser for First Contact, which came out in the summer of 1996, didn't have any exterior shots of the new Enterprise. All of the shots of the Enterprise are clearly reused footage of the D. And according to Memory Alpha:
As much of the film had yet to be shot when the advertisements were assembled, footage from Star Trek Generations and episodes from Star Trek: The Next Generation and Star Trek: Deep Space Nine was included. Inter-cut with sequences from the film, the reused footage included snippets of "The Best of Both Worlds" and "Emissary".
Later trailers, however, did include such footage.