GFCI at the breaker should have the ground tied to neutral, and still have grounds on the outlets (tied back to the GFCI at the breaker). Current through the ground pins will trip the GFCI, rendering the system safe. Since the ground pin should be bonded to any exposed metal (e.g. aluminum laptop case) a fault leading to a "spicy touchpad" should instead shut off the entire circuit at the breaker.
Just slapping a GFCI in without that bonding won't do anything though. The ground would be floating, and thus wouldn't ever trip the GFCI. There would be no path through the GFCI for the fault current to take, making the system just as dangerous as having an ungrounded conductive case.
A "double insulated" system has non-conductive material for the case of the electrical device and only needs a two-pin polarized plug. A fault of live to case won't cause danger, because the case is an insulator. A fault of live to neutral will just blow the device's internal fuse (or trip the breaker if the device has no fuse, but the breaker is just to protect the romex wiring in the walls so the device could well be on fire by that time).