Will chews affect a dog's hunger level?

It has nothing to do with the chews. It has to do with you spoiling them with "extras" in their food. You have taught them that if they do not eat, yummy things appear in the food. No healthy dog will starve with food available, so you need to stand firm. When they get hungry, they will eat. The chews MIGHT make them hold out a little longer, but in the end they will give in if you give them no other choice.