Conveniently, you can look up battery discharge curves from the various manufacturers.
The NES takes about 400mA, although any given cartridge will add something to that.
This is so much higher than
any 9V battery is capable of, it's not going to turn out well.
9V batteries have astoundingly high parasitic resistances (because they're made of stacks of six AAAA batteries).
Extrapolating from the graphs available from
Energizer:
* Eveready 1222, Energizer 522 - about an hour
* Energizer L522 - about 2 hours
* rechargeable NH22 - maybe as little as 20 minutes
If you really want a portable NES ... use a LiIon battery pack. And bypass the 5V regulator. (do NOT bypass the 5V regulator unless you're only delivering 5V to the NES logic board)