This was not the purpose of flying into the cloud.
The link between radiation and cancer was established in the '20s, and certainly well-known (if poorly understood) by the time atomic weapons were developed. For instance, Muller got the Nobel prize for this work in 1947.
https://en.wikipedia.org/wiki/Radiation-induced_cancer#Histo...
Certainly, safety rules weren't as conservative and stringent as they are today, but it's silly to think US soldiers were routinely and openly used as guinea pigs.
This is pretty important since you can both evaluate your weapon, and also to calibrate your instruments to use when collecting downwind of Soviet tests. Thus you can evaluate their weapons too.