Not really. The platform-to-platform time from LA to SF is going to be, at best, a little less than three hours. That's comparable to the time it takes to fly from LAX to SFO plus the ~30 minute BART ride to downtown SF.
LA is so spread out that departing from LAX or Union Station doesn't make a big difference. Most people are going to have to fight traffic to get to either location.
Having an extra track at the station and timing so that they pass while the other train stops. You don't have services every 5 minutes so that works quite well usually. Worst case the express train has to go a bit slower before but they tend not to go at maximum speed so can catch up again later.
