Make sure the top is up.
But seriously,
I'm sure the top would not leak as it is very well designed, has a small surface area and is generally very tight. However, convertible top or not, there are some overall issues associated with automatic car washes.
1. Damage form prep people (used at some car washes) with their bug removal brushes.
2. Harsh soaps that will strip away wax.
3. Potential equipment failures during the washing process.
4. Recycled water - used by many car washes to conserve water.
I know some of these car washes advertise the fact that they are "touchless", but at some point something has to touch the surface of the car in order to remove the dirt. And that is generally where the trouble begins at "all" car washes.
Just my opinion - Remo