I would guess no...
If a hen doesn't get the proper nutrients she needs, her eggs won't turn out as great, they can become malformed, and might end up without any shells, among other things. When a hen eats something, she absorbs the nutrients, and some of that goes into making eggs, and some of that goes into energy to move. If a hen continually eats her eggs, less and less of the nutrients will go into the eggs, as she still needs to keep some of that nutrients for energy. When hens eat things, they poop some of it, so some of the meal goes there... They might be able to survive a day or two eating nothing but their own eggs, but it wouldn't last long...
