The steam from the reactors is NOT distilled water. It is boiling water with entrained corrosion products, corrosion control chemicals, various fission product particles and gases of all kinds (both radioactive and not).

So maybe one of the first questions is - what is your water source? Reactor plant coolant/steam? Rainwater? Sea water? What? Makes a huge difference.

Distillation will indeed concentrate the particles in the boiler. As long as you don't drink from it and don't concentrate so much radioactivity that you can't approach it, you ought to be able to drink the distillate.

Or not. This is the internet. Everyone knows an answer of some kind.


(I'm speaking as a nuclear trained submarine operator relying on some common sense physics. We were never trained to treat radioactive water to make it potable. But if I were in the situation, I'd go with distillation. )