That's a good question. I don't see anything ethically wrong with it. If the chickens are just let to roam around freely like in a permaculture setting or wild. And if the egg is just going to waste anyways and they don't eat it. Or fertilize it. I don't know anything about hen cultures and when to tell if an egg is fertilized. However if we are talking about wild eggs, then why limit it to hens. There are plenty of other birds out there. Just because the western culture has limited the foods to only a few animals. Chickens for eggs, cows for dairy etc.
It would be a lot more ethical then dairy because for that the animal has to become pregnant and the food is meant for it's baby.
I've seen chickens eat their own eggs, or rather they let their babies and young ones eat the eggs.
I'd still consider the person vegan because to me veganism is about cruelty free and non-exploitation, which the situation would be. Nothing living is getting hurt or abused or exploited, so it's still within the vegan ethics. Nutritionally it's not a vegan plant food, but ethically it could fit within the lifestyle and principles.
As far as nutrition goes, I guess they could provide some B-12 and DHA that is often lacking in plant food. I don't know what else. I haven't had an egg since well, 14yrs ago when I was a teenager. I don't know if I would have the appetite for them. But if they were just going to waste in that situation I would give them to somebody at least who would appreciate them, most likely my dogs!