I have not tried a GFCI on an unbounded ground, but it might partially work. A modern GFCI outlet is watching two things:
1) Differential current between Hot and Neutral of 7ma or more. This should continue to work.
2) There are corner cases where there could be current on ground without a differential current on hot-netural. Through tricks with harmonic ocilation, the modern GFCI is able to detect current on the ground wire when there is no differential current. I suspect this function may not work or possibly trip if there is not bond.