GFCI and an Open Ground

As has been stated, a GFCI trips when it detects an imbalance between the hot and neutral. The ground has nothing to do with it. The only reason there's a ground connection at all on a GFCI outlet is for the third pin safety ground for the three wire devices plugged into it. If you look at a GFCI circuit breaker for example, it only has an internal hot connection, and an external neutral connection. If you look at the eight schematics included with this 1998 GFCI patent for instance, notice that in every case, the ground is simply a pass through with no connection to the detection circuitry at any point.