Can I plug a keyboard into a PS2 port labeled for a mouse?

As an experiment, I dug up an old desktop with PS/2 connectors, connected the keyboard and mouse backwards, the keyboard did not light up or work while in the BIOS, Windows loaded and the mouse or keyboard did not work, the Windows hardware wizard said it installed a new device and to reboot.

I rebooted, but still they did not work, so I hot unplugged the devices and connected them to the proper ports, the mouse still did not work but the keyboard came to life. Both worked after another reboot.

So no, they will not work when connected to the wrong PS/2 ports on a desktop computer.

Next, I connected a keyboard to the PS/2 mouse port on my old Dell Latitude D600 notebook, booted Windows XP, the keyboard does not work or light up any lights, and the hardware wizard did not show up.

It's a bust. No, it will not work.

...end of smoke test...

According to Wikipedia probably not:

The pinouts of the connectors are the same, but most computers will not recognize devices connected to the wrong port.