I'd like to provide some insight, from a coach who has coached 2 different high school squads in the past.
Throughout most of my cheerleading career, I was in and out because of a back injury that happened at the age of 11. When I was 15, competing level 5, I was told by my doctor that I could never cheer again. Obviously, this was heartbreaking, and I could no longer cheer with my squad. I turned to coaching as a way to continue being part of the cheer world. I starting coaching with the rec program that introduced me to cheering, and continued to stay active in my all star gym. I can still base/back a little, and can only spot tumbling. So coaching was perfect, because I could teach kids how to stunt, spot for tumbling, make choreograph, ect. Now I still coach for the rec-program, and I coach 3 teams for a small all-star program. Just to clarify, I coached for high school squads when I was 21 and 24, but now I mainly focus on allstars and coach rec on the side.
I never had the oppurtunity to be on a worlds team, cheer in high school, cheer in college, ect, which were all things I planned on doing, and what a lot of parents expect in there kids' coaches. So when I was asked the same question you asked, I answered honestly, what clearly is what the coach neglected to do. But it was uncomfortable, because I worried that the parents would want someone who had had the high school and college cheering experience, even though I still know a lot about both. When I answered honestly, I won these parents over, because they knew my passion for cheerleading was immense. The coach made a mistake by not answering, and don't hesitate to question if she really can properly coach a squad.
Obviously I don't know this woman, but I would take the time to get to know her, because I would bet she would have a reason for not sharing her background. Hopefully your athletic director would not hire someone so inexperienced, but if you are really worried, ask him or her. Their responsibility is to provide the best coaches for your kids, and you have every right to ask him for a summary of her background.
Hope this helped!