I have budgies and a lovebird as well as coturnix. The lovebird gets everywhere and into everything. The quail have been hatched from eggs and have never been outside. I still try to keep them apart but the cage birds have free reign of the room and they land on the quail cages and the lovebird has even picked up quail poop once. (I know I'm playing with a loaded gun here.)
Frankly, the cage birds are 1st class citizens and the coturnix are livestock. They are still my pets, but if I had to choose, I would chose the cage birds over the coturnix in a second. (Sorry, guys!)
In your case, I would worry that the quail could pick up something from an outside bird and bring it inside to your grey. The quail may not look sick, but they could be carriers. Anything from mites to Newcastle. Since birds hide illness until it's too late, I would be concerned that they might be sick but you not know it.
Also, coturnix have funny poop, sometimes soft and sticky (and smelly) and sometimes formed with the normal dark and white components. It's hard to use their poop as an indicator of illness like you can with cage birds.
I can't wait for Ducky to crow like a quail though!