It's probably obvious by the way I'm framing the question that I don't know much about how radiation or nuclear weapons work, but did anyone who was in the Enola Gay end up suffering from radiation related illnesses after the detonation of the Atomic Bombs over Hiroshima and Nagasaki?
After dropping the bomb at high altitude, the plane turned and flew away from it. They were around 8 miles distant from it when the bomb detonated. So they were well outside the range at which radiation would be harmful. For a weapon the size of the Hiroshima and Nagasaki bombs, you'd need to be closer than 2 miles from ground zero for the radiation to be something you'd even be remotely concerned about, and around 1 mile or closer from ground zero for it to be something serious. The acute radiation effects drop off very quickly.
They also kept at a very safe distance from the radioactive mushroom cloud that emerged afterwards.
So, no.