The fact that he deserted has nothing to do with the VA criteria for eligibility. if he was court-martialed, convicted of a crime and discharged, yep. I think that would be a problem. If being a deserter would disqualify one from getting a headstone, then half the Confederate Army would not qualify for deserting at one time or another. Many of them came back and continued to serve with their units. If I remember right, Clayton had just left to take care of something at home and would have come back except HE WAS CAPTURED by Union forces. Consequently, he did take an oath of allegiance in order to be released. In 1864, I would have done the same, rather than end up at Camp Chase Ohio, where his brother died. His brother Pleasant also deserted and was captured by Confederate forces. He was hung to death in the streets of Atlanta, one of only a couple men to suffer that fate.
I can order a headstone for Clayton. It will not be denied. I have ordered and installed about a hundred replacement and new headstones since 1990 for Union veterans, including one Naval Officer who was disciplined and discharged for being drunk on duty. No problem getting him a headstone replacement (he already had one that was illegible).
So, again, it comes down to if anyone wants to help me with this endeavor with those things that because of my geographic location or not.