So, I was going to outright reject this theory on the grounds of xx/xy chromosome determination of humans. The theory I was going to follow is that the male would effectively determine the sex of the offspring and the female will be laying regardless. BUT, it looks like chickens go by zz/zw chromosomes, where the male is the zz and female is zw. So, in this setup, the egg is technically sexed even if it is not fertilized since there will either be a z or a w on every laying, just will need that male z to actually form a chicken.
There may be some truth to variance between sexed eggs. I have my doubts that it would be as obvious as egg shape, but hopeful. Keeping an eye on this one!