No -- pay one registration, for the vehicle, then pay (at the registration trailer at the track) for a class change. The class change is a hundred bucks or so. You're registering only one vehicle -- so don't need to pay two registrations.
By the way, I think the fee for a class change BACK to what you started in costs less than the $100 -- so if you run in fuel, then change to gas, then go back to fuel -- you don't have to pay another full class change fee, just a smaller amount.