A military warrant doesn't always show on an employment background check. However, after 30 days, a more serious charge, desertion, will show. This also comes with harsher punishments. If there is a deserter warrant out for your arrest, even if your AWOL status doesn't show up on a background check, that does not mean that you're in the clear, whatsoever. The longer you remain AWOL, once caught, the worse the punishment will be. Get civilian counsel for any AWOL or desertion offenses as quickly as you can. Time is not on your side for these types of cases.