Have had King quail for a good 20yrs and no problems with the finches. In fact my mother quails will adopt any fledgling finches on the floor and cover them with their wings overnight. Can't say that this will happen with all quail, as personalitys vary.
And the cocks are ferosious little guys who will go a mouse that intrudes when they have chicks.

Again that may just be the personality of my stock, who are line-bred, after obtaining a hen who was pied about 10 years ago and trying to draw that gene out.
A warning to budgie breeders, young budgies think that young quail are toys and will play with them resulting in the death of the quail.

My mother no longer keeps anything but spare adult quail in her budgie aviary.
LML