You only need the card if you turned in the registration paperwork in the last 30 days... you don't even need to carry it past that. As for carrying an unregistered pistol, they'd need to have a reason (or your consent) to run the registration. They may stop you and run it without good reason and you'd probably lose in local courts, but with a good lawyer you should be able to get off the hook if they didn't have RAS.
You don't need ID to OC. I won't get into the complications of OC'ing in pistol-free zones. The Michigan forum would be a much better place if you want to get into details.