NO.....a GFCI continuously senses the power in the white and black wires and any imbalance disconnects.......
"Can it be the recepticle, itself?......."
YES........Carl already said to check for "backstabbed" connections they're notorious for BAD connections(Move the wires to the screws).........Also check that all the wires are firmly inserted and secured into the wirenuts.........and this can occur anywhere on that circuit before that outlet.......even in the panel........
And if this is Knob N Tube......or any "shared" neutral circuit........Loss of the neutral CAN introduce 220 Volts to a normal 110 V circuit.....
"What does the GFI do if the neutral is open......."
If you tried to install the GFCI into a circuit with an open neutral........the device will fail to energize......IT WON'T WORK........