No. If you release quail from a pen, they WILL leave, or get eaten by predators. Probably both. You need to keep them enclosed, constantly, or you'll lose them. No chicken will change that.
The reason is, coturnix quail are very stupid (bad at avoiding predators), and also are not chickens. Chickens' ancestors roost in a safe place every night, and come back to the same places. Quail just hunker down under a bush. They don't have that instinct to come back and roost.
Also, chickens raising quail can sometimes work, but it carries a big risk of pathogen transfer (chickens carry and are immune to many things that quail are not), and of the quail getting stepped on, plus you'd have to isolate the hen from all other chickens while she raised them and then put her back afterwards.