Okay,
I've worked with a lot of electricians. You'd be surprised how many only know how to WORK WITH electricity and know what the codes are, yet they don't understand the principles at hand and exactly why they work.
Ground fault circuit interrupters will trip when the sum of all current entering and leaving the gfci, through leg a, leg b, or the neutral does not balance within a few milliamps it will trip. A ground fault occurs when current has found an alternate path to ground.
Reminds me of a recent conversation I've had with some one.
Say you have a 4 wire service, and you have 2 heating elements of equal value. One element is attached to Leg1 and Neutral, the other to Leg2 and Neutral. And lets say each element has a value of 1200W, so they each draw 10A a piece from their respective Legs.
Here's the question, if both elements are on where is all the current? Common sense would say, 10A on Leg1, 10A on Leg2, and 20A on the Neutral right?
Wrong. If you measure the current running through the Neutral you would see 0 Amps. Current is flowing 10A from Leg1 through Leg2 via both elements. This is because the load is balanced. When the load is out of balance, you will see the difference in current on the Neutral. So if you turn off one element you will see 10A flowing through the Neutral.
Since either leg is at opposing ends of the wave form, if L1=100V then L2=-100V, you can measure the sum of the current flowing through each leg since they will be opposing as well. Then the gfci adds the current on the Neutral. If the Sum of L1amps+L2amps+Namps will ideally equal 0amps, if it is greater than +/- 5(ish) mA something is leaking.
As you can see the Neutral does not need to be present for a gfci to function as long as the load across the 240V is balanced.
Thats the nuts and bolts of a 240V gfci and you can take it to the bank.
If you only have a 3 wire service for 240V then I recommend you do not split the legs into 110V, if it is a three wire system the Ground/Neutral should go straight to the ground/neutral bar in the main panel. Consider it ground. I don't like to mix services but this is one of those situations where I would rather have to pull a separate 110V source with dedicated Neutral than to mix ground and neutral.