[pmangels17]

Firstly, I'd like to re-emphasize what was said earlier about standoffs, so the plates are held at a constant distance apart and aren't flexing independently of each other. Additionally, I would make sure that all your bearings are supported all around them, because from the image, it looks like the bottom bearing might be a bit close to the edge (I can't be sure, it just looks that way).

Anyway, here's a little bit of food for thought, to toss around before you lock in your final design.
Have you prototyped this setup? Have you done the math/experiments to show that the shooter is able to intake balls as well as shoot them? I would be concerned with getting the required torque for intake and also the high RPM's required for shooting, but it doesn't mean it won't work, just that if I were you I would want proof that it will work before I spend a lot of resources on it. Is there a plan for keeping the ball in the robot/shooter without contacting the wheels once it has been picked up, so that the wheels can spin up to speed before you launch the ball?

I hope this gets you thinking about design more critically. The concept you designed is definitely a neat idea, and certainly one that could work, as long as the specifics are done right.