I doubt it. It won't fix the fundamental problem of moving lots of people to where they want to go in the city. You can only do that by making the area undesirable to go to for whatever reason (probably not a good option), or by providing some alternate means of getting places. Unfortunately, due to the sprawling way LA is laid out, all of the other options are even worse than driving there.

In a dense area like Manhattan, transport is not so bad because walking, cabs, or the subway are all viable alternatives in many cases.

In a lower density sprawl area like Los Angeles, cabs are prohibitively expensive for most trips, the subway usually doesn't go anywhere near where you are or where you want to go, the buses are stuck in traffic like any other vehicle, and walking is dangerous (due to the lack of pedestrian-friendly sidewalks in many areas) and would take many hours for each trip.

I think the best way to fix LA traffic would be to greatly increase the density and start building upwards so that walking and public transport become viable options for many more cases, but that seems very unlikely to happen anytime soon. It'd take decades to do anyway. So for now, it looks like LA is just stuck with its insane traffic status quo.

The best way to fix it would be to build SkyTran. It's even being developed not that far away at the NASA Ames Research Center.