If you have the shop paint it, I would have them prime it too. I wouldn't want them blaming me if the paint didn't adhere or lay right since the right prep work is really important.
I know the guy who owns the shop I would have paint the car, and I have been using the primer he reccomended to spray parts taken down to bare metal so they don't rust. I was thinking along the same lines, wich is why I asked him:-D