It actually doesn't feel much like a dungeon crawl to me, but I'm probably like 1/4th of the way in and just having cahoots negotiating with demonsAbsolutely, and it has a good story to make your grinding/NPC-order-talking suffer-able; however, at times it feels additive to Persona 2 Innocent Sin, which is the prequel.
I liked the 'city' feel in P2EP a lot, where you had massage parlors and street vendors and aromatherapy as well as a range of food places to bum around at.