From my experience, what usually happens is that the deserter gets busted for some civ violation, like a traffic ticket, and when the cops do their NCIC check he pops up as a deserter wanted by military authorities. They hold him and chasers pick him up and escort him to wherever (I think for the Corps, they bring them all to the brig at Quantico) then courtmartial him, suspend the sentence, and give him the DD Boot. If there is a delay in court-martialing him, and the guy is compliant, sometimes they'll stick him in a uniform and have him working in an admin shop or out painting rocks.
ETA: I seem to remember one case where a guy deserted six months prior to his EAS to go home and take care of a sick family member and years later he was picked up and was allowed to finish up the six months before getting a GENDIS. But the guy had been a waterwalker prior to deserting and he got a sympathetic court.