If you are not listed as an additional driver on someone else's car insurance, but the car has full coverage, what happens if you get into an accident while driving the car?

Auto insurance follows the car not the driver, per se. So the car insurance the owner has would pay for the damages done, no matter who was driving at the time (assuming permission was given). Now the insurance company paying the claim would want to know why that person was using the vehicle and whether or not that driver needs to be added to the auto insurance policy.