In my experience (this may or may not be actually true in all cases, but it's what I've found in my daily work):

The PS2-to-USB adapters only work for mice, and only for certain kinds of mice with their internal electronics specifically designed to work as both PS2 and USB.

USB keyboards only work when plugged into a computer whose BIOS supports USB keyboards, and the keyboard must be native USB, not an old PS2 keyboard with a USB plug.