I would say so, but the only way to know for sure, short of opening it up, is to look at the input current waveform with a scope or some other device. PC (excluding laptops) power supplies without active pfc will have switches for 110/220 operation, but it is possible to have an automatic switch (transparent to the user) that performs the same function (unlikely here, but possible).
I would say, if it isn't near egg-frying temps, try it on the inverter for a few minutes and see how hot it gets. If it really is just a plain square wave (not a simulated-sine), there is a very small chance it could be damaged under certain circumstances, so proceed with caution.