All three consoles are perfectly fine for going for the world record. The GameCube Gameboy Player and the DS have the same load times. The Wii-U is slightly behind in terms of loads (about 5 seconds max for the whole run). All Emulators have very quick load times in comparison to the consoles. Emulators are completely allowed to run on, however, when you get to the point that you are very close to the world record please move to a console. The world record run cannot be played on an emulator. The reason for this is that the time advantage is far too great.

Wii-U, GameCube GB Player, and DS load speeds are demonstrated in a video by Dalton. Load times are compared by 50 door transitions.

Emulator and Console differences are demonstrated in this video by 0xwas. Again this is shown by 50 door transitions. Details of this test are said in the description

Does this apply to individual level runs, as well?

Yes.

Thanks :)

Also, if I don't yet have a game boy player, could I do the ugly version and film my gameplay with a camera?

Of course, there's no rule against it. Record with your camera if you like to

Cool. It probably wasn't worth asking, but thanks anyway :D

Does this count for Boss Endurance as well??

Boss Endurance uses an in game timer so I don't think so, just a shot of your end time

Another example discussed previously is with mGBA which loads rooms much faster. Needless to say this should not be used for your runs due to how significant the differences are

I'm probably terrible with gauging but I just tried the door thing with my original gba compared to gpsp and the load times look to be the same, I'm far from 100% on that though and wondering if someone could test it better than I?

Halodude generously gave me his console video. So I tested 50 doors again with different setting, which involves bios.Interestingly, emu's accuracy is greatly improved. But I don't mean to encourage to run emu or claim to change rulesets. (Actually, I prefer console than emu)

Lol I use my gba