It seems "City of New Orleans" was actually written by Steve Goodman, not Guthrie.
Yes, it is correct. City of New Orleans (S. Goodman) has been covered by Willie Nelson, Arlo Guthrie, John Cash, Judy Collins, and many others.
Steve Goodman also wrote the perfect country and western song, also with a train in it, and equal parts of truck, prison, rain, momma, and getting drunk.