If they can swallow it, they can eat it. They may already be able to eat bigger insects than you realize.I know they already do eat insects, but I mean like medium to large insects without more than 3% plants
The easiest way to have them be able to eat bigger insects is to breed bigger quail (or ones with bigger mouths.)
Most quail have limited access to insects. If you can arrange free-choice insects, I'm sure they will eat a lot more insects than most quail ever get to.