Sure, if that's what you want.

To get it to light up, these type of switches almost always have separate contacts for the LED itself. So it's a simple matter of finding a 12 volt source and taping into it. For a PC, you could tap into the molex power connectors used for the hard drives. If you don't want to butcher the cabling, buy a simple extender such as the one you can find at
NewEgg for a couple of bucks and cut that up. Then use the
pinout diagram to determine the correct wire to tap into (use a multi-meter to be safe).
Personally, I would get a 5v LED and draw from the 5v line. But whatever you want to do.