The device will boot and not have any damage with mixed input power. One of the jobs of the power supplies is to take input AC voltage and convert it into the form needed for internal use by the device (typically low-voltage DC), so the insides of the switch will never know the difference. Having said that, I would be cautious about mixing power supply capacity, and mixing input voltage/frequency. Mixing power inputs loses determination. At least easy determination.
What you're ultimately trying to accomplish is the ability to lose any single component, and continue operation. That means your most-capable component would fail, and your device will continue to operate. What defines a capability, for power supplies? The amount of power they can provide. Bigger power supplies provide more more - but also, higher input voltage supplies more power. So if your low-voltage power supply can, by itself, run everything on the switch (including all PoE/PoE+/UPOE), then sure get a second power supply at a higher voltage.
But if that's the case, and with a realization that all Cisco power supplies support both the 110V and the 220V standards, where would you find yourself in a building that has both 110V and 220V power available? That's an unusual setup.
Ultimately, if you can run with a single power supply running on 110V input, and if you have two independent power buses, then knock yourself out.
