If the object it touches is solidly connected to the equipment grounding conductor, there will be a low resistance path for current to return back to the source which results in rapid rise in current and the instantaneous trip function of the overcurrent device will respond and open the circuit.
Ground fault circuit interrupters primary function is not to protect from this kind of fault, but to sense current flowing outside of an intended path and trip when that current reaches a certain level - which for class A GFCI protection is a pretty low current level - in the 4-6 mA range.