After looking in the Jedi Academy source I wonder what extent this could be done. There's already homebrew ports for Wii
for the first Quake which assumes the accelerated bits of the console are already figured out.
Plus the engine already has bits of PPC code for optimization
Granted, textures would need great reduction (like down to 256 max) and sounds may need to be loaded as 4-bit ADPCM somehow just to fit in the memory. Jedi Outcast for the Gamecube compromised in texture detail and cutscenes (which were pre-rendered from PC instead) to save on memory usage for the levels. Q3A for the Dreamcast compromised by less map geometry, 15/16-bit reduced textures, and 11khz 4bit sounds for everything that's not a weapon.
The Gamecube isn't a PowerVR PCX2, so I can expect it to handle lightmaps and detail textures OA can throw at it.