I will give you 3 scenarios
1: You are plugged in to an outlet with a DOUBLE INSULATED power tool and there is a neutral to case short.. Normal or reverse polarity, NOTHING bad happens. since its double insulated. YOu are safe
2: Tool is not double insulated, and some idiot broke off the 3rd pin.. Been nice knowing you.. Depending on several things you could easily be dead if it's reverse.. Normal no damage.
3: HOT wire to case, as in 2,, but normal polarity, Same as 2.
HOT wire to case, 3-rd pin present and propely grounded, CLICK of darkness (Breaker trips) you are safe.
GFCI, may not work if reverse connected and thus may not protect you.
TRUE STORY:
Bought a trailer, 20 amp twist lock, inlet,, Prior owner made his own adapter,, Well he reversed both it and the extension cord he made it from (He cut the plug end off an extension cord and put a new plug on what's left and the twist lock socket on the pig-tail)
Plugged in with his cord, Rverse-Reverse = normal so it worked fine
Plugged in with MY 12ga 100'er.. Liked to knock me on my ... er... pride.
Things that should have been at ground were, in fact, 120 volt.. But the safety ground meant some things were at ground.. Like the metal sink.
Finally I fixed the adapter.. Then I used HIS cord and .. Fixed it.