Here is the CVC section info" Vehicle code section 4604 (d) (3) exempts vehicles described in VC 5004 from the Planned Non-operation program. VC 5004 describes vehicles of historic value ("at least 25 years old and of historic interest"). It does not say that the car has to be registered under 5004, just has to meet the description.
Yup, but you have to bring it up, and may have to push to have the branch manager come and clear it up for the counter person.