Sorry, Your post was actually really good, and I like the idea. However, I had to nit-pick on this, thats not Science Fiction, its science fact. Got a Kettle? Boil sea water, Capture water vapour, wait to cool and reform as liquid, tada - Drinkable water. I think the radiation would also be negligable.
There are desalinisation plants in gulf nations and Australia doing this on a large scale.
Ah, well you learn something new every day
I guess the sci-fi part comes in the fact that such a thing would have to be available on a large boat floating in the ocean and available to thousands of people who require it, so that essentially when a tap is turned on in the boat, the water is safe, I don't know if this exists currently, I assume submarines for example have to take their own supply with them, they're not just turning on a pump and bringing the ocean water inside, but having never been in a submarine I guess I don't know that for sure.
Within this setting (either for a Fallout game or another game where the premise is that land is barely habitable and someone had the idea of moving out to sea), there's all sorts of possibilities for conflict (someone attempting to sabotage it, either similar to the ending of FO3 or in a completely different way, or just threatening to destroy it if they aren't given something they want, not allowing certain people like the ghouls access to it, etc). It would be an interesting Fallout DLC for one set close enough to the Ocean for that to make sense (I don't think the courier is going to be walking from Vegas to the coast of California to hop aboard something that will take them out to sea).