QuietRock in Listening Room

In general, sound transmission control and sound treatment are two separate issues and have little to no influence on each other. If you want or need "sound proofing", looks like the quiet rock may help www.thespruce.com/does-soundproof-drywall-really-work-1821484 but likely have little to no effect on room acoustics.

IMHO, even if you don't need it now, it's a good idea to at least consider "sound proofing" if you're at the building phase were it can be more easily done. Later, it may be nearly impossible to go back and pull apart you entire room if your situation changes and you want to reduce sound transmission. I also recommend checking out this book: www.amazon.com/Home-Recording-Studio-Build-Like/dp/143545717X for more details, you may find you can get good results with other isolation techniques using regular drywall.