GFI does not care how many wires you have involved. It can be a hot and a neutral (standard 120V), two hots (240V w/o neutral), two hots and a neutral (240V w/ neutral), or 13 hots and 7 neutrals (?).
All the GFI does is watch the current flowing in and out of the system across all of the wires present. If the sum of current going in matches the sum of current coming back out, then the GFI knows that all is well and power stays on.
If it ever sees a different between current in and current out, then it will cut the power.
If your neutral isn't connected to anything, the GFI will still work. Nothing will be flowing in or out on the neutral line, and the GFI will just be ensuring that the two hot lines have equal and opposite currents.
BUT....
The "test" button on the breaker MIGHT be making use of the neutral for it's functionality, so you would need the neutral connected (pigtail to panel) in order for that button to work.
Question: If the ground is tied into the pigtail neutral, and a short to ground occurs from the hot leg that the neutral is paired with, wouldn't the short go through the neutral wire of the gfci and defeat the gfci protection.
1. Current going through hot lead in one direction --->
2. Short to ground occurs, and the ground is tied to the neutral in the spa panel.
3. An increase in current now going through hot lead -------->
4. Because neutral is tied to ground, increase in current also going through neutral in other direction <--------
5. Net sum of current is zero. ( amps ---> + amps <--- = 0)
6. Gfci does not trip