I think the drywall is necessary for a finished room appearance. Yeah it is a lot of work. After drywall was up i wouldnt apply fabric because it will hurt your resale value, a little ambient light is a good thing, and removing the fabric will demolish your drywall. Yes, absolute black gives best picture quality but you wont care after you smack your shin walking into the coffee table. I think sound efficiency is moot because you will easily get it louder than you can stand in that small room.
Putting up fabric directly just wont look polished.
Put up your furring strips, run your cables, then drywall and paint. Better still, hire the pros for the drywall, its grueling to do by yourself.