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I've made it clear the penalty for dropping the hairdryer in the toilet is having to run up a flight of stairs into the garage to reset the GFCI. ...
I would not expect it to trip the GFCI as I have never seen a hair dryer with a 3 wire cord. In the absence of an EGC in the hair dryer cord, there is no current path other than hot to neutral when you drop it into the toilet.