When someone is arrest while in the military, does the arrest go on their criminal record?

I am applying for a CCW permit in Louisiana and was arrested, by a MP, when I was in the USMC over 8 years ago. I received non-judicial punishment for my actions.

When Louisiana State Trooper's perform the background check, will the arrest show up?

Also, are military arrest with no convictions reported to the FBI?

Thanks...