The neutral pogtail on the breaker is for the Test circuit of the breaker. The breaker electronics will still check for imbalanced current without it being connected, GFCI protection is not that easy to disable.
I recall doing some experimenting with a Homeline 2 pole GFCI one time. Seem to recall I couldn't get it to trip at all (on GFCI function) if neutral pigtail is not connected. Still closed the circuit for output when switch was "on". Would guess thermal magnetic function still the same as a standard breaker and that neutral won't matter for those trips.
Also seemed to recall opening ungrounded conductors ahead of the breaker, and (can't remember which side) but the GFCI logic circuit seemed to only be associated with one pole, could not trip on GFCI function if that pole lost power.
It has been a while since I did this, but that is what I recall happening. Might need to do it again when I get a chance to refresh my memory.
Of course that neutral pigtail also carries neutral current when you have a load that utilizes a neutral and is not for the breaker electronics only.