No. This is just a pervasive myth started with the Ameraucana chicken when its introduction started a craze for blue eggs. As is the notion that egg yolk colour (easily faked) easily determines nutritional value. The nutrition of chicken eggs (and they are an incredibly nutrient-dense superfood that we eat daily) depends solely on the size of the egg and yolk, the diet of the chicken, health of the chicken, and the amount of sun exposure the chicken gets for increased Vitamin D3.