Can you operate a motorized scooter in California with a class C drivers license?

No, legally you need an M2

Hey stan did you just copy and paste without reading your citation. What I gathered from it is that you need an M2 not an M1 for a scooter.

No. you need a class M1 for a scooter.

California Vehicle Code 12804.9...

(H) A motorized scooter.
(I) Class C does not include a two-wheel motorcycle or a
two-wheel motor-driven cycle.
(4) Class M1. A two-wheel motorcycle or a motor-driven cycle. Authority to operate a vehicle included in a class M1 license may be granted by endorsement on a class A, B, or C license upon completion of an appropriate examination.
(5) (A) Class M2 includes the following:
(i) A motorized bicycle or moped, or a bicycle with an attached motor, except a motorized bicycle described in subdivision (b) of Section 406.
(ii) A motorized scooter.
(B) Authority to operate vehicles included in class M2 may be granted by endorsement on a class A, B, or C license upon completion of an appropriate examination, except that no endorsement is required for a motorized scooter. Persons holding a class M1 license or endorsement may operate vehicles included in class M2 without further examination.