I'm not sure how I feel about this, since part of my GAL was this new hobby and now she is doing too. Although we are doing it separately.
Who knows! If you both end up sticking with it, it could be a shared experience that you both enjoy. There is nothing wrong with that! While learning to fly, you both will definitely experience and learn about many things that you can talk about together. If she is really interested in flying, I see this as something good. If you guys didn't have a shared history and she was someone you were interested in, you would think this was pretty cool, right?