If the plug was on a GFCI outlet, it would trip once neutral and hot are shorted.
If it wasn’t on a GFCI outlet, it would be an inefficient water heater. Current is inversely proportional to resistance, and the inch of tap water between both conductors has a significantly lower resistance than the human sitting at the other side of the tub. At American voltages of 110V, the worst thing that will probably happen is the wires heat up from the current passing through them. Now, if it only had the live wire exposed and you had a metal tub, that might be a different story…