Berman hated the Dominion War and they had to fight Berman vehemently just get as much of the Dominion War into the show as they did manage to. If Berman got what he wanted the war would have been over in 4 episodes total for the whole series or there would have been no war at all.
There was not much inkling of anything good in the first season, just a TNG rehash. Yes there are a couple of episodes that are exceptions to this, but not many. Berman is to blame for this IMO; he co-created DS9 as a lame TNG rehash with no character or plot development whatsoever (just like TNG), then the other showrunners evolved DS9 way beyond that in spite of Berman (esp. when his hands were more full mucking up Voyager instead of DS9, starting ~ around Season 2 of DS9). The war in DS9 is just one of many aspects of this.
I don't agree DS9 would have been more 'action/adventure' with no war though. TOS was action/adventure. TNG was anything but action adventure, and so too would DS9 have remained anything but action/adventure if it had stayed it's (vastly boring) original course. Likewise for VOY, which lasted 7 seasons despite having almost no action/adventure.
I would say yes, DS9 would have lasted 7 seasons with no war, given that it had better ratings than Voyager and Voyager lasted 7 seasons despite having no war and being a far, far less interesting/less good show than DS9 (regardless of DS9's war arc being present or not). Thought it certainly wouldn't have been as much of a masterpiece of a show, or as entertaining, without the war.