I don't think so, yet... I was told (lord knows where) that it actually takes more fresh water in the treatment than fresh water gained. Something like that, the bottom line being, you lose fresh water.

But, I think they're taking a look at it, which leads me to think A) I was wrong, or B) new developments have occured.
http://www.reuters.com/article/idUSTRE54D6M420090514

Either way, there's lots of evidence that LA is straining things. The water level in the central valley is down dozens of feet, the Salton Sea is a wreck, even driving past some of the recreation areas built around lakes show dozens of feet drop in their water level markings. A few years ago there was some talk about running piping from the Great Lakes out towards the west coast. Last I heard that idea got firmly rejected.