I would think that if you screw up disarming a bomb, personally, it wouldn't make much difference if it were a nuke or plastique
Tho with a nuke *you* may die anyway from radiation exposure even if you succeed in disarming it.
From the story.
"They did so knowing they would likely die trying because even if the bomb did not go off, radiation poisoning could kill them."
As to radiation killing them? I don't know. I'd guess it would depend on what type of bomb it was. A dirty bomb, yes, it would likely give them a very large dose even if they managed to disarm it.