I have never heard of a ceiling comming down due to latex paint, but I suppose if it was saturated and the popcorn texture not propoerly applied, it could happen.
Most latex paint is low odor and dries to touch in less than one hour. As Steve says, you can go to the paint store (sherwin williams, moore paint spot) and get near zero odor paint. Not only that, but those guys will help you with your concerns. Its how they stay in business.