Theoretically, a true power factor correction circuit won't care what the input voltage waveform looks like; it will shape the current drawn by the downstream load to match it.
That said, some PFC controller ICs seem to choke if presented with anything but a sinusoidal voltage waveform (e.g. - UCC28070, which, let's just say, has not been one of the more glorious ICs to come out of Unitrode/TI).
If you want to go to the trouble of figuring out whether a particular PFC device can deal with a MSW inverter, check the datasheet for the PFC IC to see if it can handle a DC input (e.g. - UC3854, which *is* one of the more glorious ICs from Unitrode/TI).
All that said, an MSW inverter may damage any kind of load that isn't mostly/purely resistive and you don't have to pay too much of a premium anymore for a pure sine wave output so why take the chance?
NB - Seems T3sl4co1l beat me to it.