I strongly advise against driving a convertible through a car wash. You'll probably get away with it, I have a couple times over the years, but you run a good risk of the back window and the vinyl section it's attached to detaching from the main section of top vinyl. The high pressure air dry puts a lot of stress on that part.
Ever seen another convertible going down the road with the top up and the rear glass blown halfway into the back seat? My guess is that most of them had a bad day at a gas station car wash.
It's expensive too to have an upholsterer to sew one in.