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nevsquare:
A GFCI without the ground pins being connected to an EGC should perform its intended function. I will qualify this statement by saying I have only analyzed one model and therefore I can not say that there is not some model that might exist that requires an EGC. However, a well designed unit would not require the EGC. I doubt that any GFCI would get a UL listing if it required an EGC to work, but I have not seen the UL specifications.
Will you get a shock under some fault conditions? Yes. Maybe any conditions will produce a shock. Will the device prevent death? In most cases death should be prevented. A person with a very weak heart or other heart conditions might not survive. You should be better off with the GFCI than without it.
Is there any difference if the ground pins are connected to the EGC? Yes. Especially if the device with the fault problem has its case, enclosure, exterior surface connected to the cord ground pin. In this case if you are on the outside of the device you are not too likely to get a shock. If the leakage current to the enclosure is moderately small, then the EGC will not differ in potential much from earth. If it is a dead short to the case then about 1/2 of line voltage will develop on the case. But with a dead short the GFCI should trip within 1/2 to 1 cycle. I have not test one to see what is the shortest time to trip.
If you can get an EGC to the outlets, then do it.
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