The ceiling wont colapse, it will be supported by rafters stretching the whole length of the room, linked to others.
The plaster on the other hand might collapse. Taking the floorboards up wont help as they will be nailed to the rafters. Although, removing them will allow more air onto the plaster to help it dry. Be warned the art ex/ plaster wont be the same once dried normally. Soak up as much water as you can with towels and hope for the best.
Open windows and put heating on slightly to help it dry.
Actually, if water has collected under the boards you might want to lift the boards to soak it up. Is it your place or your parents? Insurance covers such things.