"Pvt. M. Bates, present June 30, 1864, enlisted March 2, 1862 at Spring Place, Ga., by Capt. Crook for 3 years, recorded as absent without leave on the muster roll dated June 30, 1864"

He was not listed present, but correctly listed as absent without leave on the muster roll dated June 30, 1864.

There exists the possibility that he took dutch leave to return home for a visit. While there, he was apprehended by Federal troops and listed as a "deserter."
We do not know.

I did a Goggle search of Arkansas Confederate pensions. I do not see one listed in his name, it would have been filed by a widow as he died before Arkansas pensions were allowed.

Given that possibility, we cannot prove that he did desert.

Is there any indication in his family lore of post war association with the Union of Confederate Veterans (UCV)?