Water Cycle 101: The oceans are salty because rain water has been flushing salt downstream for billions of years. Salt also collects in endorheic basins such as the Great Salt Lake and Mono Lake, for the same reason. Rain clouds form primarily from evaporation of ocean water, which leaves behind slightly increased salinity, although its effect is widely geographically distributed.

There’s a difference between that distributed evaporation and the concentrated salinity increase of effluent from a reverse osmosis desalination plant or a hypothetical hydrogen plant, but the basic answer is yes, leave the salt in the ocean. It will be fine.