Sorry, Joe, but I have to agree with Kale.
First of all, the EGC has no bearing on GFCI operation. A GFCI detects only one thing: a current difference between the two circuit conductors. If a person is truely isolated from earth, and from any grounded surfaces, and they grasp a tool with a hot-to-case fault, they won't trip the GFCI.
Since no current is being diverted from the intended pathway, they also won't receive a shock; there's no current path through their body parts. Now, the hard-wired EGC is a different story. That is there to operate a standard breaker, or a fuse, as a result of a direct-to-ground, full-current fault.
Losing the EGC pin leaves the tool case floating, and if there's an internal hot-to-case fault, only a GFCI can sense the shock current level, and not require an over-current device to open. The difference is the current required for operation; breakers and fuses require amps; GFCI's require only shock-level current.
In other words, standard 3-pin grounding methods operate to prevent the shock hazard, while GFCI's operate by sensing the shock.
