No, not completely. Most of the city was damaged by the civil war in Rapture (during the events of BioShock 2 Multiplayer). Many parts were flooded by the cracks in tubes and walls that made Rapture leak, but the Rosie Big Daddies managed to fix some of the leaking with their rivets, thus keeping the city alive. At the end of BioShock 2 the Persephone Penal colony (where the last level takes place) was rigged with explosives by Sofia Lamb's followers, and when the bombs exploded the whole prison fell into a rift in the ocean floor. Persephone was the only part of the city that was destroyed by the explosion.