GFCI's will work just fine with voltage drops, whither it is a breaker or receptacle version, the design of the circuit in them consist of a bridge rectifier feeding into a resistor voltage divider network with a ziner diode to maintain regulation of 26 volts, but the electronics will still function between 22 to 30 volts, the voltage drop would have to fall below 22 volts before there was any kind of problem.
I have worked on Tech power isolating supply's for server rooms that have GFCI breakers and with only 60 volts to the neutral buss, 120 volts line to line the power to the electronics in a two pole GFCI breaker is always line to the neutral and they work just fine at 60 volts.
Long runs on the load side of a GFCI can be a problem as was said from the capacitance and or any leakage in the circuit, and or the type of lighting use such as HID type that might exhibit more leakage then incandescent.
Here is a link to the most common chip used in most GFCI products:
National Simiconductor LM1851 GFCI IC