Is the ground socket of a GFCI receptacle that isn’t connected to ground useful? (I'm in the United States, if it matters.) If the connected appliance had current on its ground pin, where would this current go in the ungrounded GFCI? If the current on the GFCI's hot and neutral are equal, including the case in which both are zero, will this ground-pin current cause the GFCI to trip and disconnect its internal hot, neutral, and/or ground? Which one(s) will it disconnect? Can current on the ground pin keep draining somewhere even after this tripping? If so, does that mean GFCI automatically internally bootlegs/bridges its open ground to neutral under these tripping conditions?
Can the ground socket be used for grounding the following ground-pin-only items?
a shielded ethernet cable's drain wire that's inserted into the socket via a ground-only plug,
surge protector power strip,
anti-static wrist strap