Sound quality will probably be fine, the main thing to be weary of if you use Bluetooth, for anything other than music and phone calls, is lag. Depending in the implementation (codec, buffer size) you’ll see anything from 30 to 200ms of latency. Lips may be noticeably out of sync in videos, and game audio may be disadvantageously laggy. “Gaming headphones” that are wireless come with transmitters specifically designed for low latency so they’re on the low end of the lag scale where it’s not really noticeable, but your average Bluetooth implementation will be very noticeable.