Real question: is this a problem? I assume a chicken would eat eggs if you cooked it. Seems like it would eventually stop working because of physics, but is there another reason why a chicken couldn't eat eggs and keep producing more eggs?
Chickens definitely can and do eat eggs. Ideally cooked, good protein source for them.
However, you have a big problem if they discover they can crack eggs and eat the contents. They go crazy on them and it's difficult to get them to stop.
If you have this problem, leave one of those stone eggs in the nesting box to help them break the habit.