Quail adopting chicks, is this possible?

There is a big difference in temperament from bird to bird (and also between different species of quail, you might want to specify). If she is truly broody and sitting tight in the eggs and have done so for a couple of weeks - and the cage is suitable for housing chicks, then I'd give it a try, but be prepared with a brooder to raise the chicks yourself and don't introduce the chicks to her unless you are able to watch her for the next day or two.
I think I'd attempt to introduce newly hatched chicks at night. If you can do it without scaring her off the nest, that would be best. By morning, hopefully their sounds and movement have activated her instincts and she'll be the best mother in the world

 

Most mommas want to mother and will accept them.