When I write resumes for transitioning military personnel (pilots and others), I do not put the rank on their resume. For the most part, HR personnel have no idea what your rank is, as many have never served in the military.
As for organizing an event, such as an airshow, I do put that type of experience on the resume. If it is valuable experience, different from your regular duties, it shows initiative, management skills, and going "above and beyond."
Employers do like to see this information, and I consistently include it. The reason? You need to show what makes you different than the hundreds, if not thousands, of people you are competing against for the same position.
I also prep people for interviews, and sometimes these extra duties can make for good "tell me about a time when" stories. It can also make for good "talking points" when the HR person has nothing else to ask you.
Good luck in your transition!
Kathy