The more things change, the more they stay the same.
When I returned from Asia in 1976, I tried to ship nunchaku in my baggage. No go. Against the rules.
The funny thing is, they were not locally made. I bought them mail order. From a mail order house in New York. City. I had the original packaging and receipt, too, for proof they came from the States. They were for practice. They were made of foam rubber with a 1/4" lightweight wood dowel in the center.
Some rules make sense. Some rule enforcers don't. The over-enforcement or under-enforcement is a crap shoot. I had, like, $12 at risk. A treasured personal firearm would be tough to lose to either the vagaries of war or the officious arbiters of military regulations.
Your (issue) duty weapon will be well-maintained (you will be primarily responsible, with an armorer to back you up). A privately-owned weapon will not. Ammunition will be less a problem is it is an issue chambering.
A few years ago, many of our fighting forces had body armor and even vehicle armor provided to them from family members, friends and volunteer organizations because the services didn't. Fortunately, that situation is better now. But at the time, I am sure the local commanders, being practical, approved of the non-General Issue gear (some manufactured on site). I served in Civil Engineers, including a RED HORSE Squadron. Expedient methods of construction is second nature to me, and our shops people were always up for it. But that was born of necessity.
As has been pointed out before, today's war zone is different than WWII, Korea, Viet Nam. But if you have your commander's blessing, you are golden. But I wouldn't risk a personal firearm on the chances of getting an amenable C.O. And even then, you are putting both your military careers at risk, using non-approved weaponry. What you can get away with, with luck and stealth is not necessarily a good idea.
Better to become proficient with your issue weapon(s). I had no respect at all for the M-16 until I lived with one for a while.
Kudos to you for electing to serve.
Lost Sheep