The reason that Caps Lock doesn't come up in Quake III is that Quake III "maps" functions to keys, and it returns the keyboard to a neutral state (no caps lock on, no number lock on, etc.) every time it launches. Quake III "takes over" the keyboard in the sense that it prevents the caps lock key from activating caps lock, so the light never comes on.
It seems from this that it should be possible to prevent the light from coming on through some sort of software, I don't think anyone's written an app to do it yet.