No they don't. I'm a veteran.....they don't take convicted felons, because they aren't legally able to be armed with a weapon again. Once you are a felon you can't bear arms in the military......ARMY anyway.....not sure about Marines. During my last deployment we had a guy who was called up but had a felony conviction, therefore he was not allowed to deploy with the rest of us......essentially he was discharged.....
Military accepts misdemeanors, but not felonies.
Army Reserves does. I know for a fact. Its pretty much a one way ticket to Iraq as a foor soldier, but its an in if you're die hard.