It's not that I'm discounting the theory (believe me, I'm not), but I also think it's a valid theory that some improvements of the Galaxy-class were not dictated by the Dominion War and just were already in place.
But I do believe that the Galaxy-class ships we saw in the Dominion War didn't carry any families members but carried more tactical & medical personnel...but as far as them being transformed into essentially "Battlestar Galacticas" each with dozens of starfighters, I don't quite see that (shuttles would still be needed, even just as evacuation vehicles). As deep-space vessels, they'd still need science equipment, although it would be for tactical analysis & research and long-range intelligence-gathering purposes. And while we saw Galaxy-class ships deployed like capital ships in mixed fleet operations, individually, they'd probably serve as troop transports like the alternate Enterprise
did in "Yesterday's Enterprise."