Actually, if a GFCI is installed, it does not need the ground circuit to operate correctly. So what is needed is exactly as the NEC requires: each outlet must be of the GFCI type.True, a GFCI does need to be connected to a circuit that has an equipment grounding conductor to operate as designed by the manufacture. NEC Code allows in the case of a two wire branch circuit with a two wire receptacle, the receptacle can be replaced with a GFCI receptacle. The GFCI receptacle will operate just fine.
10-03-14: Atmasphere
The reason the GFCI works is because the two wire branch circuit is fed from a Grounded power system. The two wire branch circuit consists of one hot conductor and one grounded conductor, the neutral. If a three wire cord and plug piece of equipment is plugged into the GFCI receptacle and a ground fault occurs from the hot conductor to the metal case/enclosure of the equipment the GFCI will trip open when about 5 to 6 milliamps of ground fault leakage current is detected.
In the case of a two wire cord and plug connected appliance/equipment if the hot conductor comes in contact with the metal case/enclosure the case would be hot with respect to ground, a 120V nominal potential. If a person were to touch the Hot metal case/enclosure and come in contact with a grounded object current will flow through the body. If the current flow exceeds 5 to 6 milliamps the GFCI will trip open.
NOTE. A GFCI will not protect a person from a line to line, (Hot to neutral), contact.
You can see from my post above why a GFCI will not operate as designed when connected to an “Isolated Power System” where the secondary is floating above ground. The GFCI needs a reference to ground to operate.
Jim