Since only a few vehicles (most of them are pick-up trucks) can be glued on, I believe we should be able to shoot while we are glued.
Just like this:
I don't know if it will affect the cop-crim balance negatively, but glue-able vehicles are very few and they are considerably slower than most vehicles plus the police can use /cargrab command to shoot from FBI-Ranchers ( which is bug abuse I've been told)
While we are at the topic of glueable vehicles, Picador ( the vehicle in the spoiler below ) should also be glueable since it is a pick-up just like the bobcat.
Thank you for your time and feel free to leave your thoughts below : )