YOu know the egg eating hen thing is funny. A quick google only brings up how to cure egg eating in hens (culling the offender apparently :P) and I know I had one egg eater in my flock, but she died a couple of months ago :(
Tried to find something about it being harmful but couldn't.... damn sites only interested in stopping them.
I don't THINK it would harm them, not in the same way as feeding animal derivatives to cows and pigs does.
I asked about this when I visited Sunny Day Farms & she said that feeding the eggs back can extend their short lives. We were talking about genetically modified turkeys, but I imagine it applies to chickens. That or the dogs eat the eggs.