Yeh, because the weapons designers at Aldermaston would not think of putting the chicken in a separate section. Moreover pecking at wires is unlikely to set off a bomb.
It sounds outlandish, but it does have some logic to it. Other proposals involved insulating blankets, but those are not remembered because we can't make fowl puns about them.
That insulating blanket idea seems like a cover-up to me.
Hmm, a dinosaur descendant, living that close to a radiation source. Ah, the possibilities...of B movies at least.