No,they don't. And beyond that,they now throw out military members who have been convicted or even charged with "domestic assault" because of the new laws that allow the police to steal the guns from anyone charged with this crime.
No they don't. However, you may be interested to know that if you are convicted of a felony, then the charge is later reduced to a misdameanor, dismissed, and expunged. You have NOT been convicted of a felony for all purposes (including joining the military) EXCEPT you can NEVER own a gun.