Depends how many they built and how much stock you put in the TM, but there were three hull losses in the first 8 years, and we didn’t see any newer ships with families on board.
No.
The TM is not canon or “canon.” The shows pick and choose what is. There are other “official” TM’s; they’re not canon either and have also been contradicted by what’s on screen.
The Federation (and likely any power of your choice) lost a lot more ships than three in those eight years, and most weren’t Galaxy Class.
The Yamato was lost to superalien tech that if not for a Galaxy Class would have destroyed a D’deridex also.
The Odyssey went into danger without non-essential personnel, lasted longer than most ships would have, against a millennia-old super-empire, one that had been spying on the Federation for some time, succeeded in its mission, was only destroyed by a kamikaze attack of a large ship (in the episode), and only blew up after drifting a moment even after that. It was a beast.
The Enterprise was lost to spy tech with no(?) casualties.
We have no idea how many ships (Galaxy, bigger, or otherwise) are out there with or without families.
We do know that the Galaxys were heavily featured during the Dominion War, none were seen destroyed, and some were seen kicking serious ass.
We know that Admiral Riker was still cruising in the old Galaxy Class Enterprise in AGT, and Captain La Forge commanding a maybe newer one on VOY.
And we know that, out-of-universe, TNG’s ratings remained higher than other Trek series on at the same time. I think some of that comes from the promise of the future represented by things like families in space.