If he was apprehended by Federal troops, listed as a deserter, and subsequently released. Then, I would believe he truly was a deserter and released from Federal custody on taking the oath of the US.

Otherwise, he would have been held as a Prisoner of War, and shipped to a Union prison camp.

I believe normal practice would be to list those AWOL for a number of bi-monthly muster rolls as AWOL, then finally having not returned, dropped from rolls being listed as a deserter.

If they were truly aware that a soldier had deserted, then he would immediately be listed as so on the next muster.