What counts as "power failure"?
This is similar to functions found in the bios of PC's as described here. I don't believe that functions is supposed to be available on portables, but evidently it is for you.

What explicitly counts as a power failure is loss of power to the motherboard. So that means the battery would have to be removed while the MagSafe is not connected. If the MagSafe is connected, it would not count as a power failure. 

The computer starts up again if the power was cut to it (Last State). So if you yank the power at the log in screen, it'll power back on however if you yank the power after shutdown, it'll stay shut down.