I'm a military brat and i've dated a buttload of those dudes... it's very tiring.
I give you props for your PATIENCE GIRLY!!!** Patience, breathe.
I can tell you right now that he may or may not start right away. If he doesn't start the camp right away, then he may get the letter before camp starts and be able to instantly respond. Otherwise, if it's the first week of camp, it'll be about a week before he can respond or even read. Some recruiters hold the mail all week until Sunday... Otherwise, the best day to reply IS SUNDAY. Which means, more than likely he'll send you about 1 letter a week. If you had been married, he may have been allowed a phone call too, but i'm not sure about that one.
Expect 1 letter a week, maybe 1 every two. They get more lenient after about 4-5 weeks.