In most if not all cases, this would be covered under the dealer's coverage. In most states, they will only ask for proof that you have a driver's license, I can't recall ever being asked for insurance papers. It may not hurt to shop for insurance for the particular car model you are buying, so this can be factored into your monthly budget as you buy the vehicle.
If something were to happen while you were test driving the vehicle, I'm not saying that you couldn't face some litigation. But I'd make an argument that the "deeper pockets", that of the car dealer, is going to be at the front of that line.
