Okay, first answer. Yes you can do what you are looking to do, however, you will want to wire the lights off of a relay and use the factory fog circuit to trigger the relay. LED lights have a tendency to bleed down slowly causing a weird strobing effect that oscillates back and forth (two separate lights). If you like light shows, go direct, I opted for a relay and that eliminated the strobing. You may have to cut a plug off the harness to gain access to the wiring for the relay.
Simple answer - if you can handle a basic relay control, then yes, you can do what you want to do with little fuss and no additional wiring from the battery.
Some folks are fine with being screwed over, perhaps finding confrontation to be more stressful than just living with whatever the problem is. These are excellent consumers, manufactured to the finest specifications.
Reformed Jeep addict... Jeepless for now.