I have a basement theater with a similar type of ceiling you are describing. In my case, the ceiling is constructed from plywood, wire lath, then about 1 1/2 inches of concrete serving as a bed for 3/8 inch thick quarry tile. In between the ceiling joists is fiberglass insulation. Below the ceiling joists in the theater is an acoustic suspended ceiling.
I hear lots more sound coming up the stairwell than through the floor. In fact, I can be immediately above the screen/speakers and still can hear more from the stairwell 20 feet away than through the floor.
My home is also three levels. My bedroom is on the upper level. I can barely hear the theater from the bedroom at normal listening levels. I cannot hear the bedroom TV from the theater at all.
I would say that if the expense was not too great, then go for it. It will lower the sound transmitted to the rest of the house.
J. L.