Yes. I believe the DS9 people wanted to have one in the background or even on special occasions, but the execs wanted to keep her for the movie outings. Frankly I think it would've been just fine to see the Big-E in a shot or two, sorta like seeing the USS Galaxy in action at Chin'toka. It WOULD seem a little wierd to have Picard in a fleet commanded by Sisko, but it's not as though the hierarchy of the big fleet battles made that much sense to begin with IMO, beyond cool-lookingness.
I agree that there probably weren't that many Ambassadors built to begin with, being supposedly akin to the Galaxy's initial rareness as Starfleet's premier explorer. However, where the Galaxy may have seen increased production beyond the six that were initially planned (per Sternbach et. al.), the Ambassador may have been kept to small production runs and also to their intended duty of being deep space explorers.
I like to imagine maybe two dozen of the class being constructed in two batches (NCC-10xxx and NCC-26XXX ish, going by known registries) and spending the vast majority of their times on the periphery of Federation space and beyond. When the war rolled around, Starfleet may have recalled those Explorers within a year's travel time of the conflict, but otherwise left the guys further out on their own, perhaps at best telling them not to go out further on their planned courses into deeper space just in case they needed to be brought back. We know that Starfleet had ships up to thirty years travel time beyond Federation space (VOY "Lifeline"), and one or more of them may have been an Ambassador-class ship, tooling along and waving the flag to anyone who may want to come conquering. :P