Soldiers that were wounded severely enough often were furloughed home so as not to consume already stretched resources of their regiment. Even the medical care was transitory, with regimental surgeons, assistant surgeons and hospital stewards moving with regiments. Battles would cause these medical officers to be detached from their regiments as they set up field hospitals that would remain until soldiers could be moved to larger hospitals, sanitary commission hospitals or... to be sent home to their families.
Ergo, home was a likely alternative which caused extended absence for a soldier. Also there was a difference between officers and men, and distance. Other than the 8th Kansas Infantry and, to some extent, the 7th Kansas Cavalry and 1st Kansas Battery, most Kansas troops served primarily in near enough to Kansas that troops could go home.
I have several examples of men who went to make-shift hospitals, then were moved to Fort Scott, Fort Leavenworth, Kansas City, etc. and then to home. My great-granduncle, Private Culvin F. Tracy, 15th Kansas, was sick at Fort Scott, which was close enough to his home in New Lancaster, Kansas, that his wife Lewisa Tracy, tended him at the hospital in Fort Scott. Colonel William Weer, 10th Kansas Infantry, (then the 4th Kansas) gave himself leave to return to Wyandotte, Kansas in October 1861 for almost a month to "recover from his illness".
The example you gave, CSA and Georgia to Ohio, is unlikely as most southern soldiers were alienated from returning to northern states and communities.
Hope this helps,