The AC line has to have at least two functional wires to work: a 'hot' and a 'return', or Line & Neutral form a complete circuit through whatever load is plugged in. Usually, it doesn't matter which side of the plug is which, because it goes to the primary of a transformer. Trouble happens if one side of the AC wiring is tied to the chassis. The Neutral eventually goes to Ground back at the main distribution panel, so a short between the chassis and the Neutral is not a good thing, but not necessarily dangerous. The Safety Ground pin is just that: a direct path to ground to drain off voltage that becomes shorted to the chassis.

If the connections get reversed (easy to happen with a 2-prong plug) it could mean that the chassis, and anything touching the chassis, is now at Line voltage, looking for a path back to ground. You do [u]not[/u] want to offer yourself as part of that path! This is why all modern 2-prong plugs have one prong that is larger than the other one. This larger prong will fit into the Neutral slot of the outlet, but not the Line side.

All of this becomes moot if you have an older plug with equal-sized prongs, or there is a problem with the extension cord.

There is no safe way to operate equipment that has the chassis lifted up to Line potential. Don't do it!