> Is the damage similarly picturesque if it's set to 240 V and plugged into 120 V
Unlikely to have any effect, as the PSU would not start up until it has sufficient voltage on its input stage.
Worst case would be that the 3.3V and 5V rails power up, while the 12V rail has maybe 8V instead. I suppose in this scenario a HDD might fail to spin up properly and have a "head crash". So still potentially catastrophic for some hardware, but unlikely to damage most hardware. I think ATX mandates a "Power Good" flag to prevent startup before the power rails are at the expected voltage.
Whereas with the switch in the wrong position at 240V, then the electrolytic bulk capacitors and front-end voltage regulators end up with twice the voltage they were expecting, and explode, violently. With a -really- old power supply, the fried voltage regulators could "fail short", and pass 30V or more along to the supply rails and fry every component in the machine. But on anything since the 80s the exploding part is on the other side of a high-frequency transformer, driven by electronically "chopped" DC. An isolated SMPS can't "fail short", because the transformer can't pass DC. If the fuse doesn't blow then the transformer would burn out, with potentially lots of smoke and/or flames, but the other PC components -should- be fine, assuming your house isn't on fire at this point.
----> safety goggles required if you want to test this on a junk computer
Schematic of a pretty awful PSU of this vintage that I found on an image search - note the 110/240V switch, and the lack of any precise regulation on the 12V and 5V rails!
The 110V/240V switch connects one leg of the AC to the middle of the bulk capacitor (2 capacitors stacked in series), which effectively doubles the voltage. I'm simultaneously baffled, impressed and horrified at how this works.