Actually, I hate to burst the myth, but a curtain, even a thick one, isn't a great sound absorber. Does it absorb sound? Yes. It absorbs pretty high frequencies only. There just isn't enough dense material to vastly improve the sound in the room. Heck, most commercially available absorption panels are covered with a fabric that is about as thick as curtain fabric. When calculating the absorption efficiency, they don't even really count the fabric covering into their calculations since it is not really good for absorption.
With that said, I am not saying that you shouldn't do it. Half of the basic room acoustical plans say to make the front wall (screen/TV wall) "dead" and the back wall stays "live". Plus, like you said, you can close off the space more for reducing light coming in, etc.
I made my front wall dead with absorption, but still added a thick panel on my back wall and it improved the bass response in my room. It took a decent sized 5.5" thick absorption panel to do it though.
I just wanted to make sure that you didn't focus too much on the curtain being a "great" sound absorber, but I would still do it.
