When crossing the Continental Divide either on the Southwest Chief or even on the California Zephyr, one is not at the highest point for too long, and one is typically not exerting while there. It would be very unusual for someone in otherwise good health to feel any effect. In general even in hiking in mountains they always say "explore high, sleep low", the idea being that try to sleep at a lower altitude that you are acclimated with, but feel free to travel high during the day. But none of that really applies to crossing the continental divide on trains. You are not at the high altitude long enough for it to matter that much.
Now if you were traveling by train to Lhasa it would be a different matter, and that train carries Oxygen to relieve altitude sickness. But we are talking 13, 14000 feet there for extensive distance and time, and a highest point of 16,627'. I have been on road trips that high in Tibet and in Ladakh in India. For those, it is better to be first acclimatised at at least something like 10 or 11,000'. Otherwise at least it is very uncomfortable the first few days, and sleeping can be very hard at night.
