Army here,`no harm in trying it now. Not sure how AF Basic is, but it's not going to be Primal. After you leave training you'll have a lot more control over your diet.
As far as staying Primal, it's certainly doable. It's a lot easier in the AF, you guys get Hilton's and catered meals LOL. But there will be times when you just have to suck it up and eat what you can.
AAFES is getting better about stocking healthier foods, but you'll find you'll still need to go off-base to like Whole Foods or something similar.
"Go For Broke"
Fat Kine-230/24% @ 6'2"