They could. If they were hatched together, than they're more likely to get along.
If the quail were really small like button quail, than the chickens would probably kill them. Coturnix, maybe not kill, but it's likely.
But it's best not to keep chickens and quail together in a roost, barn, etc. Due to the risk of a disease which chickens carry that is lethal to quail and vice versa.
Chickens would most likely pick on the quail due to their tiny size any way.
It's not really safe to introduce young 'man-raised' chicken chicks into a flock, so nor would it be for quail I guess.
Correct me if I'm wrong, but it's better to be safe than sorry.
I just read an article in this months Hobby Farms Magazine(Chickens) It says no. It seems they catch cocci really bad from chickens.
They really do look interesting. All kinds too.
I am sure those with more knowledge than I on quail will help you more. Like I said I know chickens but only book knowledge when it comes to quail.
Come on those who really know and help us out here. Gloria Jean