Did you try it? I didn't know better and tried it long time ago. Cast iron skillet that was used for years. After few times in dishwasher significant chunk of seasoning was gone.
While stainless steel is “dishwasher safe”, dishwasher detergent is still overly harsh, can cause discoloration, and will prematurely wear the pan surface.
Dishwasher soap is a whole different story. It contains abrasives, among other things.