In every house I have seen, the neutral is bonded to the ground at the panel box. If you connect a GFCI-equipped power source (eg: generator) to a circuit with a bonded neutral you will trip the breaker because it is designed to trip under those conditions. That means that you cannot connect such a generator to the panel box. You also cannot connect it to anything that may have a connection between the neutral and the ground that will allow more than 5mA of current, which at 120VAC means approximately 24,000 ohms of resistance. A lot of appliances and fixtures can experience that amount of leakage current, and refrigerators are among them.
Disconnecting grounds is not a good idea under any circumstances, and you can still get a pretty good shock from a GFCI protected circuit under some conditions, particularly if you have created a floating neutral by removing the ground.
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