It's from a different song, Steve, but may have been possible by taking a connecting train to Kansas City. Though this question really has no effect on the veracity of the song, since the song was from the movie, "Harvey Girls" which was set in about 1903. "Atchison, Topeka, and Santa Fe" is the name of the railroad line, or was until it mergered with the Burlington Northern in 1994--not the name of a route. The line was chartered in 1859 to run from Atchison to Topeka. It was extended to Santa Fe in 1879. In many places, the route followed the old Santa Fe Trail.

The Super Chief, El Capitan, and other Chicago to LA trains ran along the main line of this famous rail route, beginning in 1926, but as far as I can determine, by this time the Atchison part of the route was no longer on the main line(though Topeka is--Santa Fe is on a spur line which is now operated at a tourist rail line-- if you are traveling on AMTRAK, you get off the Chief at Lamy and there is a bus connection to Santa Fe)

"Harvey Girls" is about the young women who were recruited and trained to work in Harvey House restaurants, which offered elegant dining that was affordable for rail travellers. They were placed at appropriate intervals along the Santa Fe line and were stocked with fresh food items brought in on the trains, which made them highly appealling to the locals as well as the rail travellers.

There is a depot in Atchison, which is now a museum(famed aviator Amelia Earhart was from Atchison) but seems not to have been a Harvey House. I left a message for to the curator of this museum asking when the last passenger train service stopped(a freight line coming up from Kansas City is still active, but is part of the Union Pacific RR--the track that once went to Topeka is now out of service, and may even have been removed). I think that it is more or less a seasonal kind of thing, and he may only be there on weekends.

Anyway, this is an important question, and deserves an answer:-)