Well.. We have a male duck that will eat his own offspring the first few days, till they get too big, should he get the chance. I could try to explain that biologically by some far-fetched explanation about him perceiving that the ducklings will become his direct competitors for food or females in the future, or that he simply lacks protein in his diet, but to me it just seems plain stupid ^^
Your quail doesn't necessary have to be directly attempting to kill the chicks, to cause their death. They might just be curious and try pecking at them to find out what they are - and then peck a bit too much. Or they might step on them. Or the chicks might go to the wrong quail for heat and end up dying because that quail won't sit on them.
That being said, I have buttons - 3 hens and one roo. One hen hatched chicks, another one was broody too and helped take care of the chicks. I put the 3. hen in a cage inside their enclosure for the first week or so, because she was pecking at the toes of the chicks, but when I removed her cage, she actually ended up helping with the chicks as well. But I've heard about other buttons killing chicks that were not their own, or even button roos killing their own chicks(my roo helped caring for them as soon as they hatched).
I've never had bob whites or coturnix though, and as those rarely hatch chicks on their own, I haven't read much about how you might expect them to react to chicks - I actually don't think I've read a single account of bob whites or coturnix that were in an enclosure with chicks that were not their own. Thus, I can't say it wouldn't work - and therefore I suggest you monitor closely if you try it.
