Probably. AFAIK GFI measures the current difference live and neutral, so a current between live and ground (as in the third slot) would trip it. Imagine if some

Probably. AFAIK GFI measures the current difference live and neutral, so a current between live and ground (as in the third slot) would trip it. Imagine if someone forms a path for current between a "grounded" metal case and live. If there is no third slot then "grounding" means connecting to neutral, so GFI wouldn't trip.