Generally the USB to PS/2 adapters work, but it's not guaranteed.
1. PS/2 was spec'ed to deliver 5V at up to 275 mA (1.375 Watts). USB is spec'ed to deliver 5V at p to 500 mA (2.5 Watts). So if the keyboard needs between 1.375 W and 2.5 W to function, it'll work plugged into a USB port, but not when plugged in a PS/2 port via an adapter.
2. There are two types of USB to PS/2 adapters. The simple kind contains no logic, it just rewires the pins. These will only work with devices which are USB and PS/2 compatible (many were back when both standards were widely in use). You can see this in the product description for the adapters. e.g.
https://www.amazon.com/StarTech-com-Replacement-USB-Keyboard-Adapter/dp/B000A0K2JO
Note: This is a replacement adapter that can only be used with USB keyboards that are both USB and PS/2 compliant. If you keyboard shipped with a similar adapter than this adapter will work with your keyboard. If your keyboard did not ship with a similar adapter than this adapter will not work with your USB keyboard
For keyboards designed to be USB-only, you would need an adapter which contains logic to translate the USB signals into PS/2 signals. I spent a few minutes searching and could find no such adapter. Lots of active adapters for plugging PS/2 devices into USB, but not the other way around.
Also note that PS/2 is not designed to be hot pluggable. You often could hot plug it, but sometimes it will crash the system or freeze the system. Theoretically it's possible to damage the hardware by hot plugging (though I've never heard of this happening). So PS/2 devices should be plugged in before powering on the system, and not unplugged once powered on.