Well, unfortunately, the best answer I can give you is "maybe". Perhaps someone else will have more luck, but the issue appears to be that your ancestor is one of those that shows up in census records, but doesn't have many other clear records besides. John Clinton Holmes appears to have been married at least twice, but even then there's debate about which two of three possible women were his spouses. He was definitely in Harlan County by 1860 and for several decades after, but when he arrived is a bit confusing, because he appears in both Lee County, Virginia, and Harlan County, Kentucky in the 1850 census. My assumption is that if he served, it was probably - but not definitely - from Kentucky.
If that's the case and he did serve, then there are eight John Holmes who served in the war from Kentucky, three of whom are Union soldiers whose records have middle initials that aren't "C". That leaves two Union soldiers in the 6th and 28th infantry regiments and three Confederate in the 4th and 9th cavalry and 3rd mounted infantry regiments. I'm afraid I can't get any more specific than that, nor is there anything further that I can find indicating if any of them are this man.