I had a few shipmates that got waivers for convictions, some of them for some fairly hefty things; things like cracking into a computer in Germany, copying some pre-release software, and charging the 18-hour phone call (this was in the days of dial-up) to someone else’s account (which required breaking into another system).
If that guy could get in, and the military is a bit more desperate than they were when I was in, I think you’ll be fine.