Was it explicitly the gamma radiation in his blood that transformed Jen? Or was it some other thingy?
Rick Jones once attempted to give himself super powers by exposing himself to gamma rays and only wound up with terminal cancer (The Beyonder cured him).
Having not followed the Hulk for a long time now, the answer is not really. You can’t track him with a geiger counter. You don’t need a lead apron.
However, considering the many changes he has gone through- OTTOMH
Started out grey, changed from Banner to Hulk at night.
Green, changes when angry.
Green, but with Banner’s mind.
Green, back to dumb and destructive.
Grey again. Changes at night. Hulk changes name to Mr Fixit and finds work as muscle for Vegas mob. (Hmm during this time a character named Half Life was introduced. It was clearly stated that Half Life was radioactive. But, I don’t know if this was meant to be true of all gamma mutated beings, or just HL. HL’s powers were not radiation based. By night, he was strong, fast, and his body healed quickly, severed parts even reattached themselves. By day, he was a radioactive corpse.)
Green, changes when angry, tearing off Banner’s skin through a large scar on his back.
For a while, the Hulk was green with the green Hulk’s superior strength and abilities, Banner’s inteligence, and Mr Fixit’s nasty attitude.
I’m not sure what his situation is now.
At various times he was certainly radioactive, having been caught in additional gamma bomb detonations.
AFAIK Marvel character transformed by radiation do not remain radioactive unless otherwise stated.