Do not get overly concerned about the term "deserted."
My own great grandfather with the 5th Tenn. CSA is listed as "deserted", but he fought and was wounded at
Shiloh and later fought and was wounded at Atlanta.
However, one of the Guthries with the 34th Arkansas CSA was in the Little Rock area when he and a bunch
more deserted in May and took off for home. In the fall, he joined the Union Army.
Could your man have joined the Union forces?