Yes, it is banned. 

Dolphin was fixed a while ago to have accurate math calculations to allow perfect gameplay emulation

This is simply false. The performance of GX varies wildly depending on the performance of the PC. To verify every player who wants to play on Dolphin and submit their times here that GX runs accurately on their PC at all times is just not going to happen. The frames drops that happen could be an unintended benefit, though it can also throw the player off.

Unfortunately the ladder doesn't require mention of which method of playing the game was used. Otherwise I would imagine such times would be allowed to be submitted, but will probably not count towards the official ranking.

I specifically ment the actual math that occurs each frame, not run-time performance. I'm very aware that most people probably can't run all tracks/modes at 60fps, as well as performance drops from things like shader compilation.

Thank you for confirming that it is banned, I'll continue to keep my times to myself.

 Part of me wonders if Dolphin should get a seperate ladder.  Keep in mind that the Gamecube is almost 20 years old, at some point we'd have to switch to emulators.  I'm not sure what FZC would think about that or if it's even possible, but I do think that Dolphin records should be allowed, just on a seperate leaderboard as to not detract from records set on actual Gamecubes.  

Eventually it should be allowed, but it'll be a while before that happens I think. As it stands we have people struggling to run GBA games at full speed. It would be a pretty big untertaking to moderate it all too.
For now, we have USB loading as an option for those who have a modded GC or Wii without needing a copy of the game at least.

I agree with the idea that the console used to run GX is old, thus those who want to get into the game may not be able to find a Wii / Gamecube in order to time attack.

Eventually my Wii is going to break and I won't be able to time attack any more, which would be upsetting. A "Dolphin Max Speed" Ladder to me seems to be the best solution, but I have no idea how to prove the validity of a run.

 this "eventually" is at least 10 years or more away.

emulation in the ladder is only going to be justifiable when cheap level PCs can run the game perfectly and finding working GC/Wii consoles becomes near impossible and discs die due to disc rot.

and even in this event, the rules allow USB loaders and SD cards to get past the dead discs. consoles's internals last a long time.

we'll have this discussion in the 2030s. for now forget about emulation on ladders.

(also, this site's code is too old and convoluted to add new ladders. it's never getting new ladders. we have to wait for a brand new site)