Is that even possible? California could use it...
We could place the reactors on oregon beaches and then transport the water down to California
You cannot, directly. You could use the steam generated in a nuclear power plant to flash evaporate seawater, remove the "brine" (everything you don't want), re-condense the steam to fresh water, chemically treat it (since even the heat of boiling won't make it safe enough to drink), then pump it into the fresh drinking water system.
That's how the Navy ships with boilers or nuke plants did it, back in my day. Nowadays, however, they're switching more and more to reverse osmosis plants, on both ships and submarines. Not sure if it's less maintenance intensive, cheaper, or what the reason is.
One problem you'd have to overcome would be the lengthy pipe you'd have to lay, to suck relatively clean seawater into your system, though. The US Navy did not make fresh water within 12 miles of ANY shoreline, and fresh drinking water within 25 miles, when I was in. Why? Because not all countries have the same standards for treating human waste, and we didn't want to deal with trying to clean up water that had fecal material in it (or, at least, in higher amounts, like you'll see off the shores of most 3rd world countries). Even here, in the United States, you'll deal with ships that dump all sorts of nasty stuff overboard, once they're at sea, and it's nearly impossible to catch them at it. The further out your suction is, the "cleaner" the ocean water is going to be.
Yeah, and pretty much this. Good luck, ever getting another nuke plant built on the left coast, with all the tree huggers congregated there!