Most of my shot whizzes right through a quail. I shoot lead or steel 6 depending on regs at where I'm hunting. I'd say most shot whizzes right through the bird. You can see wound channels easily, especially with lead shot, and it's helpful to rub that wound channel or maybe stick something like a chopstick in there to dislodge any shot. Also helps to shoot premium shot like zinc or copper coated lead -- that keeps the lead out of the meat okay.
We have mountain quail here in coastal Oregon. I hunt them opportunistically once finished with archery elk season but would not consider myself a pro or anything. They are very elusive birds. Sometimes see a few, other times coveys of 25+. Very challenging terrain and probably more calorie negative than chukar hunting. Gorgeous, huge quail though. My favorite time is September when the blackberries are still ripe and be birds can gorge on them until their livers turn purple. Techniques for mountain quail are quite pedestrian. Literally, walk or drive gravel logging roads on the coast range and hope to jump a covey gritting in the road near dawn or dusk. Then hunt the covey. These quail will associate with logging roads, recent clear cuts, and creeks. Southern Oregon is the place to be for highest numbers.