This is a late response, but I saw your posting and wanted to give you a possibility. Located about ten miles south of Adairsville is the little town of Kingston, which is where the railroad from Atlanta to Chattanooga had a branch line running westward to Rome. The Confederacy established several hospitals there, one in the depot, the others probably in churches. I do not know the names, but a posting on the Georgia Board would probably bring results. There is a large Confederacte Cemetery located at KIngston, which I suspect was strictly for those men whgo died in the hospitals around Kingston.
There is every reason to think that a man who was badly wounded at Adairsville would probably have been treated at the first availabe set of hosptials away from the field, and that would make Kingston a prime candidate for where your ancestor was treated, and, ultimately, buried.
Unfortaunately, there are only three or four marked graves in the cemetery; all the rest are unmarked graves. No stones, just a very well-tended grassy and shaded cemetery located amid the woods four or five hundred yeards from the center of the little town. There is a Georgia Historical marker just outside of the cemetery which gives the names of the hospitals and the number that are buried there. I visited the cemetery 15 years ago +/-, and am stating the numbers from memory, but I think there are about 400 unknown Confederates buried there.
If your ancestor is buried there, it is a very peaceful spot. The cemetery is surrounded by a chain link fence, and is (or was) completely surrounded by woods -- no encroaching development, on the side of a hill. I do not know who was tending the cemetery, but I recall that the care was meticulous.
You might contact the nearest Sons of Confederate Veterans Camp in Cartersville; they have a web site and perhaps they can answer some of your questions.