At the risk of getting attacked by those who won't think ...
No, military service is not productive. Nor are intelligence gathering, (legitimate) law enforcement and fire fighting. These things are PROTECTIVE. A functioning society must have people doing both PRODUCTIVE work (farming, mining, manufacturing, transporting) and PROTECTIVE work (see above) in order to survive. They are different, but necessary.
If they are necessary for a society to survive, then their productivity is manifested by the society's survival. Their product is security. Because of the state of the world, they are necessary as you pointed out. Without it, the PRODUCTIVE work couldn't happen, lest we end up plowing for those who didn't beat their swords into plowshares. It is a cost to the society, but it allows it to live and grow.