I don't own a GameCube (and it would be too expensive to get one.) Can I upload a run with Dolphin if I promise I won't use any emulator cheats?

If emulator cheats aren't the issue, then I won't do the thing with the issue.

I think the reason emulator isn't allowed is because of inconsistent saving and loading times from the emu memory card, the easiest way to run is on a Wii with backwards compatibility (pretty common), an official GC memory card (59 and 251 are the slowest, and 1019 is the fastest), and then either a disc of the game or homebrewing the Wii and using a homebrew application called Nintendont that loads GameCube games from a USB.

I think it's a bit unfair that the community doesn't even bother making a seperate Emulator category, old hardware is becoming more and more expensive, for example, trying to get a 1019 memory card is pretty much an investment.

Dolphin should be at a point where it runs accurate enough to be considered competitive.