I make this statement because of several entrys in muster rolls of infantrymen being transferred to the Artillery. In a lot of these records there is no reason given for the transfers. But in a few I have found that it was because of injury and or illness. I had a Ggrandfather who by late in the war could not use his left arm becauses of wounds, but he was still serving in the army at Richmond when he was captured in 1865. But that is another story.
In one case in Arkansas a private that I have personal papers of, in the 9th Arkansas, Richard Reep, was wounded during the Battle of Shiloh with a "bullet near the spine". I would think that this would have been a pretty serious wound and would have caused him to be disabled. Well it did effect his ability to march and do other things. But about 6 months after being furloughed home he is listed as being in Owen Battery (Monticello) Arkansas Artillery.
I can only make the connection that the military authorities deamed that he could still be of service in a less demanding branch of the service, where he could ride instead of walk. I do not know exactly what his job in that battery was, but from his letters it would seem that he was not on the Gun Crews, but worked driving the wagons and caring for the horse of the Battery. In the typical artillery battery there were more horses than there were men.
I don't know whether Reep's story was typical or not. But I would imagine that late in the war and maybe earlier that even man that was able to serve in some function was employed where he could best serve.
This was the reason that both sides early in the war used slaves and freed blacks as teamsters, cooks, etc. It was to maximize usable manpower in those service where they could be most effective. This was one of the reason that Hindman dismounted most of the Cavalry and made them Infantry in Arkansas in 1862.