Actually a cheap NEON tester can tell you a LOT. It will tell you which side is "hot", if one is. (capacitive connection with your finger.
It will tell you if the ground is totally open (no "bright" light across the socket) and it will tell you if you have a significant ground problem (the ground side lights capacitively with a load plugged into the socket)
Semantics. If the "u" ground on the receptacle ic connected to the neutral, either at the plug or the panel, everythiing will work fine except the case of every grounded device connected will be HOT.
If, however, the neutral is connected to a functional ground, and the H-N wires are crossed, breakers and/or fuses will complain immediately upon power-up.
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