I don't think they'd mind it. They may eat the lower leaves a bit, but they won't strip bushes like chickens. I gather the berries are toxic to us, but there doesn't seem to be anything to say they are for quail. I even found this which says holly is safe for them:
https://green-shack.com/plants-for-quail/

If you're ever unsure of anything, just do a search on it. What you might encounter in your garden may be different to mine, but someone else will be guaranteed to have an answer somewhere.