I no longer own a Gamecube and copy of the game but have been replaying it on Dolphin emulator. I used to play this game so much back in the day that I have a natural inclination of beating it fast and was debating giving an actual speedrun a try.

There are a few emulators on the boards, and nothing in the rules prevents you from using them. I'd say go ahead.

I was running it on gamecube but I switched over to Dolphin recently because it's way easier to record. Only issue is the current ISOs for the gamecube are a little unreliable