I have one hen who occasionally lays a thin-shelled egg that gets cracked in the nest. I make scratch omelets from those as a treat for the chickens because I don't feel happy about feeding cracked eggs to the family.
If they are in need of protein - during illness or molting - then there's nothing more perfect than an egg.
So, yes, you can feed chickens eggs and there are times when they certainly need the protein that an egg provides. Young chicks like nothing better than a bit of mashed hard boiled egg.
When my chickens were ill and on medication, we were unable to eat the eggs so I would cook them and give the scrambled eggs back to the chickens. It gave them more of a dosage of the medicine plus I hated to waste the eggs.