I'd call your insurance agent to confirm coverage in this situation. I would never buy a used car without taking it for a test drive. A ride isn't enough to detect vibration in the steering wheel, etc. If the seller refuses to let me drive it, my first thought is "What are they trying to hide?" Or maybe I'll make a lowball offer to cover any hidden problems.
EDIT - My point was, if you insist on not allowing test drives, you're probably restricting your pool of available buyers, and may have a hard time getting the best price.