If he goes into Finance, the worst that can happen is a papercut. I am an accoutant so I can tell you those cuts can get nasty
One guy I knew was finance in the Army. Volunteered for nearly every deployment in a combat zone that he could. Stellar and awesome career during the peak of the OIF years, including several stints manning combat positions when they asked for volunteers. Was actually nominated for Bronze Star at one point due to combat action he took part in.
I also have known a lot of Air Force services folks were worried they would be flipping burgers and folding towels at the gym when they joined; instead, they wound up manning convoys in OEF early on.
Every military career has potential if you know how to make friends and be in the right place at the right time.