What's the use of the ground socket of an ungrounded GFCI receptacle?
Despite its name, a GFCI does not look at ground current - it only looks for a difference between the line and neutral currents passing through it.  If it finds a difference of 5 mA or so (maybe 15 mA??) it assumes some current is going where it shouldn't, and trips, disconnecting the Line and Neutral. 

The Ground pin on an outlet is intended to connect non-current-carrying parts of an appliance to Ground, to ensure the safety of users.  If the Ground pin on an outlet is not connected to anything it cannot connect anything to Ground, and is useless.