The neutral carries the same current as the hot conductor. A ground would be necessary for the GFCI to work properly.
The GFCI will still work properly without a ground (hence its acceptability in ungrounded retrofit appliations) but the GFCI tester wouldn't work, as it can't shunt a small amount of current to ground if there's no ground to shunt to. Standing in a puddle and sticking a wet finger into the receptacle aught to do the trick, though. But it's certainly not recommend as the consequences if the test fails are potentially rather dire...
