Interesting idea, but I don't see how it would reduce cabinet size.
Your bladder would have to be at a different air pressure than the rest of the cab to make a difference. I'm imagining a tire inner tube (with the valve stem sticking out the side of the cabinet

). If you have the tube at above-atmospheric pressure, you have made part of the cabinet volume stiffer. That reduces effective cab volume - the opposite of what you want. If the tube has less than atmospheric pressure, it is collapsed, so does nothing.
Perhaps others will see something I've missed.