Will a GFCI device work on circuit where the neutral is switched?
A GFCI is only measuring currents and does not care about the voltages on either of the two wires going through it.

As long as the net current is always zero, it really doesn't matter how it is switched on and off.

The real problem with a "switched neutral" is that the contacts inside the fixture are live with respect to ground even when the switch is off. If you should accidentally touch the contacts while grounded, the GFCI will protect you by tripping. But if the fixture were wired correctly, that particular risk wouldn't exist at all.