If caught, they were most likely court-martialed. I have recently received on Inter-Library Loan the "Roster of the Courts-Martial in the Confederate States Armies" by John A. Bunch, White Mane Books, 2001. Deseration makes up a large number.

Confedrate Army Regulations article 150. Deserters shall make good the time lost by desertion, unless discharged by competent authority.
Article 151. No deserter shall be restored to duty without trial, except by the authority competent to order the trial.

Note however, that a man absent for a certain period of time was recorded on his companies bi-monthly muster roll as AWOL, after another period of time this was changed to Deserted.

Unfortunately, later in the war, company muster rolls were lost to history, and we have no way of knowing if a soldier subsequently returned and was reinstated. It was common for a man to absent himself for considerable periods of time, then return.

George Martin