The rules doesn't say that Dolphin emulator is banned, so you are free to use it, keep in mind the emulator in unstable so depending how good is your pc you may or not have problems with the game, AFAIK nobody have done runs with that emulator, feel free to give a try.
As Shadow said, Dolphin is unstable as heck, but since rules doesn't have any kind of restrictions with emulators and nobody runs the PS2/GC version, feel free to run the game in Dolphin emu. Obviously when you submit your run we're gonna see how correctly does the emulation is, you need to keep care about some stuff during your run like a stable framerate, don't use any kind of tool to have better graphics and all kind of stuff like that.
Also it would be nice if you can add an input display program in order to prove that you didn't use extra tools (like prerecorded runs), it's not required but is appreciated in order to make the verification more faster
