Stunningly too expensive, according to the article they have "nearly million tonnes of radioactive water". That's a billion kilograms. Even at a pretty phenomenal $15,000 per kg to launch into space that would run an impressive $15 trillion.
And that really only puts it in low earth orbit, where it would fall back down again after a few months/years, maybe decades if you get it high enough.
Clearly the best method for dealing with radioactive waste is building a space elevator to get it out of the gravity well for cheap.