Compared to the amount of water that is naturally desalinated every day (ie via evaporation), even large scale desalination is a drop in the bucket.

Desalination is already operating on a massive scale in the middle east, and we're not seeing any medium scale effects there. Elevated salinity dissipates very quickly from the point of outflow.

I've not seen any evidence supporting this is the case, but the opposite; large swathes of high-saline concentrated blobs sweeping accross the sealife, killing it. We've had to build specialized very long outflow pipes to give the brine even a change to level