No! There is no way to detect whether an animal has been fed GM feed because there is no content from any part of the GM feed in the flesh, milk or eggs. The GM feed is digested and assimilated in exactly the same way as any other feed. There is in fact no meaningful measurable difference between GM and convention feeds.
Actually that's not exactly true. It turns out that conventional and organic feeds can have more of the mycotoxin fumonisin in them than does insect resistant GM feed. Specifically, studies show that insect protected corn can have less fumonisin. Molds that produce mycotoxin often grow at sites of insect damage on corn ears and because the GM grain has less insect damage it has less mold and consequently lower levels of fumonisin. Thus GM grain can in this instance be safer than non-GM. Fumonisin causes esophageal cancer, neural tube defect babies (NTDs) and other illness so this is an important benefit that is largely being over-looked because of the hysteria that has been created around the safety of GM crops.