No, no, no. There is no indication he deserted. He was a casualty of the Battle of Shiloh, he was there, unfortunately, he must have been left on the battlefield, died, wounded, we do not know.
The only thing we know is that he was not among the survivors of his company/regiment returning to Corinth.
In as much as we find no Yankee POW records, and he never returned, we must therefore assume he died as a result of his wounds, and is buried in a mass grave on the battlefield.