Unless they are conducting an FBI level search, they would not find this. It's not a conviction, but in most instances an arrest by the military is registered with the FBI (not always....sometimes they just fail to do it).
In some instances, even the disposition (like Article 15) is later updated with the arrest, so that the ultimate disposition is known.
However, for an employer to find this, they'd have to pay for that very much higher level FBI records search, which takes into consideration Federal arrest records. Most employers don't pay for that, instead using a search that just checks state level jurisdictions.
Now, in a security services job, that is just the sort of job that may be willing to spend the extra money and go for that higher level search. If they do, and the military did what they normally do and filed the arrest, then it would show up.
I know there are a lot of "ifs" there. Unfortunately, when you are dealing with discretionary choices (and the filing of an arrest with the FBI is discretionary), I can't KNOW what they did in your case...just what they can do.