No I don't think so. This is a very old thread. We were there in Feb of this year and didn't have that option.
The quiet area is too small, and to be honest it isn't that quiet! We sat back there last visit and it was a bit more loud than in the main room.
Reason being: The servers bang really hard on the wood door as they come and go. So if anyone is on the other side they don't smack them with the door. About every 2 mins you hear "bang bang bang!!!". It was very annoying. That space back there is small and closed in, so the sound echos. I would rather be in the main room, at least you are away from the banging.