No, although the convertible top may not leak immediately after washing it in a carwash, there is a high risk of leakage.
The canvas of the convertible top often consists of multiple layers of cloth. The outermost layer is coated. This coating is delicate and wears quickly because of the chemical and mechanical burden. The products used in car wash facilities have not been developed for use on the canvas of convertible tops, tents, sails, etc.
Thus, it is advisable to clean and apply protective treatments to the convertible top manually. That way, you avoid the risk of leaks and the convertible top will remain in better condition for longer.
Always ensure good protection in any case. You can impregnate the convertible top a few times a year with Sprayhood & Tent Protector. This product has been specially developed for impregnating boat covers and tents exposed to extreme weather conditions, and making them watertight.
See: impregnating-convertible top