Didn't see anyone answer your question so here goes. It shouldn't cause any damage to the wipers at all. They're designed to be able to wipe at 100+ mph. Maybe not effectively but work without flying off or bending. When I used touchless car washes in the past, I always turned the wipers on to let the air blow the water under the wipers off.
If you have rain sensitive wipers, they will turn on every time, lol. I always forget to turn them off when it stops raining. Could be a problem if they got tangled in a brush car wash though. (OH, I will never have to worry about that one)