It depends on how it is supported. If you are living in an apartment, I dont know how you would keep it from bringing down the ceiling. If you live in a house, attaching it to the support beams will weaken the supporting walls and cause the room walls to start cracking (personal experience).
When I had my house built, I had the contractor build a angle iron support in the basement, attached to the concrete floor, independent of the floor joists. This way all the movement of the heavy bag will be separate from the house supports. Funny, you should post this, the military hung a heavy bag in an aircraft hangar recently and the weight from the constant movement started causing the weak aluminum supports to buckle. If you rent a place, be wary, you will be responsible for the damage and support damage repair is expensive. As far as damaging the bag, if it is good quality, no, leave it up.