> The ground would be floating, and thus wouldn't ever trip the GFCI. There would be no path through the GFCI for the fault current to take, making the system just as dangerous as having an ungrounded conductive case.
GFCI works by detecting an imbalance of current on the intended path - i.e. between live and neutral. For an ungrounded conductive case to create a electrocution risk, there must be an alternative pathway through the user's body and a potential difference to create a current on that pathway. Whenever these conditions occur, there will be a live-neutral imbalance which will trip the GFCI before any harm is done. In contrast, with an ungrounded conductive case and no GFCI, if a fault creates a situation where electrocution is possible, the only thing that could protect the victim is the circuit breaker, but the breaker must allow sufficient current for normal use, which is well above the threshold for lethality.
GFCI works by detecting an imbalance of current on the intended path - i.e. between live and neutral. For an ungrounded conductive case to create a electrocution risk, there must be an alternative pathway through the user's body and a potential difference to create a current on that pathway. Whenever these conditions occur, there will be a live-neutral imbalance which will trip the GFCI before any harm is done. In contrast, with an ungrounded conductive case and no GFCI, if a fault creates a situation where electrocution is possible, the only thing that could protect the victim is the circuit breaker, but the breaker must allow sufficient current for normal use, which is well above the threshold for lethality.