I've spoken with a few oceanographers about this and the brine can be easily pumped back into the ocean with very minimal impact as long as you are smart about it. The effluent from a normal desal system is only twice the concentration of the source seawater. The key is to place your plant so you can reintroduce the brine into a fast moving and deep waterway.

One interesting ancillary benefit of having a source of brine is that it makes extracting desired minerals and elements from seawater much cheaper and easier. I have personally seen a system that extracts uranium from seawater. Current implementations yield yellow-cake at twice the market rate. There is ongoing work to tie it into a desal plant and bring that cost down. There is also work to combine it with lithium extraction.