Micpat,
I agree with Jim's statement.
The line side neutral is required for the correct operation of the GFCI electronics. However, the load can be with out neutral, or the load can be only between one hot and load neutral, or there can be multiple loads that are 120 V and 240 V connected at once.
The two hots and neutral, as they pass through the GFCI, go through the center of a torodial transformer core. As long as the instantaneous load currents on any combination of the three conductors (two hots & neutral) sum to zero, the net magnetic field around the three conductors will be zero, and, therefore, the secondary winding on the toroid core will send a zero output to the GFCI circuitry.
When the currents on the load side are unbalanced, the secondary winding on the toroid will send a proportional output to the GFCI circuitry. At an output level corresponding to a 5.0 milliamp imbalance on the load side (of the GFCI breaker) the GFCI trips.
It doesn't matter where the imbalance current goes, only that it does not return through the toroid core. The equipment ground, whether it is the return path or not, is not part of what makes the GFCI work.