Earlier quoted context omitted.
The water would rain down eventually and replenish natural reservoirs. This, of course, further limits where the plant must be located (coastal areas would not be adequate for this)
There's no assurance the water would rain down where you wanted it to. Since the Earth is radiating its heat anyway , just over more area, you're also only transferring that evaporation to specific locations (though it's possible that goethermal heat would radiate into space without heating and vaporizing water in some cases). On a net basis the effect would likely be too small to matter. I suspect utilizing the heat…
I wonder if the energy in the Yellowstone system could be tapped for that. We would at least have the plot for a really bad sci-fi movie...
Taking seawater to it would be an interesting problem in itself.