If underground populations were kept alive by hydroponics then they could move those above ground. They could move to higher elevations where the water comes directly from rain and has little or no radioactive content.
Might not be an impossibility. I don't see 100,000's surviving and being kept alive, but I could see 1000's or tens of 1000's. That would be enough to restart the population.
If the pols and generals were smart enough to save practical people like engineers, welders, plumbers, electricians, builders, survivalists, etc. then the human race would have a chance.
They'll be more likely to try to save their own worthless hides!