If you have the (unofficial) approval of your unit commander, are part of an advon, or are one of the people in charge of building the pallets/packing the equipment, then I guess I could see you bringing your personal sidearm (though illegally). When transitioning out to the AOR, you could potentially be stopping in a number of different countries, so unless you have it with the gear, if you are personally carrying it, or even if it is in your checked baggage, you could issues.
Are you flying out on a rotator (DoD commercial) or on military aircraft?
What is your specialty/MOS?
Are you going to be on a major airfield/base or outside the wire or at a FOB?
These all matter, because depending on your answers, not only would it be impractical, useless, and potentially dangerous, but it can get you arrested.
You more than likely don't need to bring a personal firearm, and shouldn't.