I just had breakfast and got really sick. I looked at the egg box and it said "chickens fed high multi grains and soy. . ." ohhhhh. So, yes, eggs can make you sick if the chickens are fed with grains and not corn. I am going to find some eggs high in corn and not fed soy or grain. I ate a different brand last week and didn't get sick.
An Ohio State University graduate student experimented with feeding chickens a diet high in soy protein to see if he could influence the amount of soy isoflavones (a component of soy protein) in those chickens' eggs. He found that he could: chickens fed the high-soy diet routinely produced eggs higher in isoflavones. (http://celiacdisease.about.com/od/glutenfreefoodshopping/f/Are-Eggs-Gluten-Free.htm)
So I figure that if rBst can effect your milk, and high soy diets can effect eggs, then what the chickens are fed can effect your celiac or gluten intolerance.
Always read the label of EACH product, and don't assume. I get into more trouble when I do that.