As Frank said, in dedicated service it would probably go back in the passenger train for quicker turnaround. Not only didn't it make any money empty, but the longer it took to come back, the more cars would be needed for the business.
For generic express service, I've seen plenty of pictures of such cars in freight trains. Also, the GN, and probably other roads, had "express" cars that looked like conventional boxcars or reefers, but were equipped with high-speed trucks and steam/signal lines. These could often be seen in freight trains, as they were used for any "high class" clean loads.