Yes, but if you want time on the train and a scenic ride you may not be happy with how they do it. In the event of a misconnect with the Coast Starlight, passengers on the Southwest Chief are typically taken off somewhere between Barstow and Fullerton, loaded on buses, and driven up to Bakersfield to catch the San Joaquin north to Sacramento or thereabouts and rejoin their original itinerary there. If that happened to you then you'd miss the stunning coastal scenery which is one of the main reasons to take the Coast Starlight in the first place.
If you were primarily just trying to get from point A to point B it might not matter so much; on an April 2014 trip I took the chance (but I was connecting from the much earlier Sunset Limited) and was rewarded with an on-time arrival in L.A., breakfast at Phillipe's, and a gorgeous ride up the coast in the Parlour Car with my father. Our main goal was to get from Houston to Whitefish where I had off-season reservations in a ski lodge for the week, so if we'd had to do the bus thing we would have still arrived in Montana on schedule. But it would have been a big disappointment to miss the coast. If you're taking the trip for the train time and the scenery and don't have any pressing need to make a same-day connection (our trip to Whitefish was booked as an AGR 1.0 reward, so we couldn't break it anywhere along the way), then I'd strongly recommend working in at least a one-day layover in L.A. Visit Mickey or catch a movie in the Chinese Theater or some such.