Yes, the trains ran regularly from St. Louis through Callaway County during 1863.
The Federals determined early in the war that they must control transportation infrastructure in Missouri in order to 1. keep Missouri in the Union, and 2. keep the territories and states west of Missouri in the Union. They permitted the original owners of the railroads in MO to continue operating them, primarily since there were mostly owned by New Englanders. Missouri railroads were not operated by the Union military as they were in other parts of the country. Throughout the war the railroads in MO were operated in an efficient manner when not affected by warfare. They were heavily guarded by Union troops throughout the war, and the Union military made frequent use of the railroads for troop movements.
Missouri southerners resented this partnership between the Federal army and the state's railroads. However, after 1861 Missouri southerners refrained from a high level of sabotage against railroad infrastructure due to severe penalties imposed by Union military tribunals on those convicted for "bridgeburning" and on humanitary concerns that innocent lives could be lost in case of train wrecks brought about by sabotage.