The interface needs to be powered off a 5 volt and a 12 volt line (unless it's a Capcom IO powered off a Jamma harness).
You could draw power from the computer for this, similar to how some people power coin door lights and stuff. But then you have the same problem: PC needs to be on to play Naomi.
So you have really two options I can think of:
1.) wire a switch so that you can select power from either the Naomi setup or the PC setup.
2.) Get a small power supply for just the IO board. Not sure where to find one. A PC power supply seems overkill for that...
If you find a solution, let me know! I was wondering how to do the same thing for when I finally get my hands on a Sega Ring-Edge.