Yes, they check-through bags onto VS. Although I'd highly recommend you speak with someone at LAX (maybe the VX baggage office) to make sure it gets handled correctly. Or wait at the carousel for your SFO-LAX flight just to make sure your bag doesn't get dropped there.

Once I did LAX-EWR-LHR and despite getting thru-check at LAX all the way to LHR, my bag ended up on the EWR carousel. I didn't see it but thats what the staff at EWR told me. Then they made sure it got transferred to VS.

So the point is, be vigilant about it.