Using Quark beta 2.0-179, the overrides appear to all be taking priority over the applied resource pack. I first noticed this with my own custom pack, but after some testing it seems to happen regardless of what resource pack I have applied. (For example I tried using Faithful as well as a few other packs I had lying around.) It’s easy to check looking at spawn eggs or music discs, or any of the mobs being replaced.

I tried placing other textures inside my own resource pack’s quark folder, using the same path: overrides/textures/item/spawn_egg.png and so on. But this also did not work; the mod insists on using its own textures regardless.