Proper operation includes the correct operation of the "Test" button, which verifies that the GFCI will trip on a ~5mA outgoing vs. return current imbalance. Depending on the internal design of the GFCI, the neutral connection may be required in order for the "Test" function to work properly. Connect the GFCI breaker according to instructions, whether you have 120V loads serviced by the circuit. or not.
Again, depending on the design of the GFCI, it might require the ground to be connected in order for the "Test" function to work. You don't need the ground for the leakage detection to work as intended, but if you can't test the trip threshold, you won't know if the GFCI will trip when it should.
A USA 240V GFCI breaker monitors currents in the two hots and the neutral as an aggregate. All three wires go thru the current sensing coil. As an example, if a load has 18A of 240V draw, and 2A of 120V draw, then one hot will carry 20A, the other hot will carry 18A, and the neutral will carry 2A. The direction of flow of the 20A hot will be the opposite of the direction in the 18A hot and the neutral. So the "vector sum" of the of the currents is zero. If there are no 120V loads, then the two hots carry the same current, and the neutral carries 0 current.
As stated above, the ground is not compared to anything in the GFCI, but may be required for the "Test" function to work correctly.
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