Australia has plentiful uranium reserves, relatively dry climate, a well-educated population, and huge amounts of empty space. Seems tailor made for nuclear powered desalinization.
I think the consensus across the board is "yup, it does, and it would help massively" though it always came down to money and how it was going to get funded.
Side tangent: I cannot for the life of me understand the argument for "well, yeah, climate change is bad, but let's think how much this might cost to fix...". When it comes to existential threats to our mere existence, how is cost a factor? Talk about the definition of short sighted! And more, it's super short sighted on the money aspect too. We make changes to what is acceptable, how we do things, and yeah, it might cost a ton to begin, but we all know from history that amazing amounts of money are to be made in those revolutions too. This is not a zero sum game.