It should still trip the immersion detector in the plug. There is a 3 wire cord in a hair dryer but the 3d wire just connects to a ring in the barrel of the dryer. It is similar to a GFCI but it is looking for any current in that 3d wire from either line side conductor.
Yes, that is the purpose of the immersion detector, I was talking about the branch circuit GFCI protection. It is very unlikely that a two wire device will trip the branch circuit GFCI when the device is dropped in a toilet....unless the toilet is an all metal one like found in prisions.
