That's pretty unlikely, given that the water systems are more of less closed, and the volume of water in the oceans is so massive that it wouldn't make an appreciable difference at any reasonable scale.
Keep in mind that this isn't the creation of desalination, just making it cheaper. There are already plants that do this at a scale of 50 million gallons a day, or under 1 trillionth of the oceans.

Localized salinity changes are more likely to be an issue, but for that I think they just mix that salt back in with processed waste water, making it roughly neutral.

will raise the salinity of the ocean

If care isn't taken to avoid concentrating brine going back in just one spot, sure that could create localized problems. Buuut, you realize that the oceans constantly lose water to evaporation and their salinity is more or less stable, right? Every bit of rain or snow that falls on land (most of which returns to the ocean eventually) is water the ocean can be without and still not too salty for life.

Speaking of salinity, the Atlantic Meridional Overturning Current (which in normal conditions, is the deep/cold return current from the gulf stream -> North Atlantic) is running into a big damned problem because Greenland is melting and all that fresh water pouring off of it is disrupting the return flow of cold water to the tropics. That's why the Gulf Stream has been so hot- it's not getting return feed from its radiator in the North Atlantic, and meanwhile the North Atlantic is getting colder because it's not cycling water back south, and that prevents hot Gulf Stream water from getting there.

Edit: I recently learned that concentrated brine regions in the oceans (called brine pools) are a thing. There are massive salt deposits (as much as 8km thick) under the bottom of the Gulf of Mexico today, the legacy of a time when the gulf was closed off from the oceans- when it refilled, the salt layer was covered over. Today, the deposition on top of it is heavy enough that subsidence within it squeezes the softer salt around, occasionally exposing that salt to the ocean water.

Which also prevents ice from forming compounding more problems(the big massive problem) which we’re trying to avoid talking about right now.

The oceans have been collecting salt from runoff for billions of years, humans reintroducing some of that salt before the water will not affect ocean salinity.