Let's not muddy the waters with too many variations. The OP was asking about the device that came with the air conditioner.... not the house wiring, or HVAC stuff in general.
I note that the NEC equates these particular devices to AFCI devices ... which suggest that they will tolerate a higher leakage current than a GFCI, perhaps as high as 30mA.
That, in turn, does suggest that there might be a problem if an air conditioner is added to a GFCI protected circuit.
Somehow these problems magically disappear if the unit is 'hard wired.'
