It entirely depends on the implementation of the PFC.
A PFC power supply is a complicated device, and it could have been designed with a square wave in mind, or it could have been designed to only work with a sine wave. As there are so many ways that it could be made, it's not really possible to have a blanket statement that it won't work.
It's quite possible that a PFC power supply will be quite happy with a square wave. With zero voltage input, the power supply can't do anything. When the voltage is steady, for a few ms each half cycle, the PFC power supply may well behave exactly as it would near the peak of a sinewave, so it could work fine.
On the other hand, there may be some input sensing circuit that will not regard a square wave as a valid input, so it'll do nothing and not work at all. I've seen that with a laptop power supply running from an inverter. I don't think the power supply contained PFC. On some inverters it just would not turn on, and would behave as though there was no power at all. I think that the power supply would be detecting the periods of no power, and they were too long. I bypassed the problem by running the power supply from the DC link voltage of the inverter.