Theoretically, yes you could. Practically, absolutely not -
An average battery in a portable, we'll say, is about 4Ah at 7.4V. That gives us 26.9Wh at 7.4V. The screen uses a linear regulator and the n64 5v line does, too, so we'll roughly estimate that as 300mAh draw on the direct power line. The 3.3v line draws roughly 1.5Ah with the expansion pak, but since you can only get about 90% efficiency with the regulator, it's equal to drawing 1A from the main line, very roughly.
That's a total draw of 1.3Ah (or so, not exact) at 7.4V, meaning that 4Ah battery will last about 3 hours.
4Ah = 4000mAh. A single 9V battery is usually about 150mAh, and for simplicities sake, we'll say it costs $1. That means for $1, for one 9V battery, you can play on your portable for roughly 1/10 of an hour, or 6 minutes. However, 9V batteries aren't good at providing that much current all at once, so a lot is dissipated as heat. Drawing at 1.3Ah, you'd be lucky to get 3 minutes of play time before the battery simply gave out. That means that you're paying between $10-$20/hour to play an n64 off of 9V batteries (depending on how you wire them (in parallel, or 1 at a time)).
TL;DR
No.