You won't know till you try. So if you are inclined, try it, keep track of what you did, and report it. Even better is if you can do half your batch in a traditional way, and the other half in your test way. That would give you and everyone you can share the experiment with a good control group to compare with.
I suspect they may not thrive due to lack of minerals/vitamins or the wrong balance of them. I also suspect if they are on such a diet, they will grow slower, be fattier, and be prone to joint/leg issues. But we wont know till you try. Just keep in mind these cornish x are a highly selectively bred cross of birds which have been grown for optimal growth on formulated feed. They may be less resistant/adaptable to feed changes than your run in the mill dual purpose barn chicken is. That said, awhile back, there was a thread on someone who split an order of sexlinks with his buddy, and there were large differences in the conditioning, weight, maturity, onset of lay between his on formulated feed and his buddies on corn.