I know of no regulatory requirement that requires a Soldier to be licensed on a piece of equipment to perform PMCS.
The licensed operator should be the individual starting the vehicle and operating it. The Soldiers who are not licensed should be taught proper PMCS procedures using the -10 and how to fill out the 2404 by the licensed operator. They could do Before and After operation checks as long as it did not require operation of the vehicle.
Most units have a maintenance class and licensing program that Soldiers must attend to ensure they are properly trained on PMCS and properly prepared to operate a vehicle.