If the mic, that was included with your computer, came from Apple, then it should work.
What makes you think it is a "non-self-powered" mic?
If probably has a longer than usual connector (pin) on it and draws its power from inside the socket.
Did you try it?
As noted; I have a G5 PPC operating with OS X 10.5.8.
I am wanting to use a microphone plugged into the Audio Line-In Port on the rear of the computer. Can you offer a suggestion as to what manufacturer and model does a nice job of laying down a voice track (no singing involved). According to the Power Mac G5 Guide this microphone would need to be a "self-powered" mike.
Which leads to a secondary question of why did Apple include a "non-self-powered" mike with the computer?