The only time I can see adding pronouns that makes even the tiniest bit of sense would be if you have a name that is gender neutral. Like Stacie or Dale and you want people to know for sure if you're XX or XY.
HOWEVER, even that is very iffy for military. We all have gender neutral terms, in the Army, Air Force, and Marines we even have two!
First rank. Second for Army and Marines, "Soldier," "Marine," or "Sailor."
Even if you are addressing someone in the Air Force and don't want to risk someone freaking out for calling an E3 an AirMAN First Class, just say A1C Jones. I've no clue what the Navy would do for the Seaman ranks.
I do the same in my current civilian job. I will just use titles for most people.