YES, You must have a valid California permit in order to get behind the wheel training.
Local Driving School can issue a student license (OL800) to students 15 years of age or older. This allows the student to drive with Local Driving School’s instructors only, before obtaining a permit. Please add a link to show a picture of the Student License (OL 800) Please review the attachments to find a picture of this form.
NOTE FROM DMV: "This licensee may issue Student Licenses to qualified applicants. A student license shall limit the operation of a motor vehicle to such times as the licensee is taking driver training in connection with the driver education program and then only at the direction and under supervision of the instructor." reference (DMV.ca.gov)