Can I hang things from a thick sound proofed wall?
The room is sound proofed by using certain sound resistant materials in a certain manner. One of the key concepts is to isolate the interior wall finish from the exterior (or other side of the wall) wall surface. In this wall, RC-8 resilient channels are used to isolate the interior wallboard from the studs. This keeps the sound waves (or most of the sound waves) from passing through the wall. 

If you install hangers, fasteners or blocking through the interior wall surface and attach it to the other surface, you may slightly reduce the quality of the isolation, but not significantly enough to be detected. I would keep the fasteners to a minimum. If you think about it, you're making a "conduit" for the sound to travel through the fastener and into the stud, then through the stud and through the wall material on the other side...exactly the opposite of what the RC-8 channels are doing...isolating the 2 sides of the wall. 

You may want to use cabinets that can support themselves so they don't need to "hang" on the wall. Then, just use a sufficient amount of fasteners to keep them from tipping over.