Most power plants do use water in their power generation, but it's largely a closed loop and freshwater is used. Fossil fuels/trash/radioactive decay is used to heat water which evaporates into steam and turns turbines, then cools and gets used in the cycle again.

If you decided to use saltwater in this process, the salt would be super super hard on the powerplant, piping, etc and dramatically reduce the lifespan and increase the maintenance costs of the power plant. You also wouldn't be able to generate water safe for use, as the water would likely be contaminated. You're better off with a dedicated power plant and a dedicated desalination plant.

Finally, you still need to figure out what to do with all that salt. If you dump it back in the ocean, you're going to kill off wildlife en masse and just generate more and more salt over time, as the salt concentration in the water you're pumping in increases. You can't dump it on land, it will completely destroy the ecosystem and you will need a TON of space. Unlike landfills, it won't decompose over time - just wash away (which means you're killing things elsewhere). You could potentially use old mines and such, but those aren't reliably structurally sound and you're still risking runoff or even worse, getting massive amounts of salt into the water table.