The relay harness does a couple of things.
- Takes power directly from the battery, rather than the lamp feed
- Takes the lamp feed and only uses it as a relay trigger
- Ties both sides together.....resulting in no left/right fire issues
It isn't so much a wire gauge issue, considering HID's are typically 30-35w draw compared to 55-65w halogen draw. It's more so a reliability issue the relay harness is solving.
Generally, fogs don't need a relay harness. I always suggest it for headlights though. Since they're on two different circuits from the factory(you have a left and a right side fuse).