If you want to use a 6V battery, you will have to change the NES regulator. If the 7805 on the NES is like any other 7805 I have seen, it needs atleast 7.2V to operate. You also can't feed 6V directly into the NES.
Maybe I could use a transformer to boost the voltage, and then use a 7805 to get it at 5v. But I don't think they make transformers to boost the voltage one volt.
And then the first human typed up '1337'. Faith in humanity soon plummited.
You could, but there would be a number of problems:
1. You would have to find a good step-up transformer.
2. It would dramatically lower battery life.
3. You would need to create an AC current.
4. You would then need to change the AC back to DC.