Nah, there are third-party Showdown servers running (Nugget Bridge has one, por ejemplo), though it looks like you may be right about the media all coming off of Showdown's own servers; I don't see it hanging out anywhere obvious, at the least, and apparently logins all run through their own server, so yeah, maybe those are all kept behind closed doors yet. Custom pokémon should be easy to add, though, I think... it looks as though there are already some in there? I don't know that there's a server actually using the CAP-mon yet, but they're right there in the code... Good point about the media, though, I don't know what would happen if you tried loading a pokémon without whatever stuff the Showdown site might currently be keeping to itself. Bah.
Eh, I'm just judging by all the "look guys I'm making a Pokémon game framework in Python/Java/C++" threads that pop up on Pokécommunity, which show like hey I already have the map editor done. And look, you can walk around and interact with NPC's! But then somebody comes into the thread and is all like, do you have a battle system, and they're like well no I'll do battles later. Someone else already did the battles! And probably better than you could on your own! (Why nobody has tried to make an open-source pokémon engine also baffles me, though I guess a lot of people are used to game programming alone or in very tiny teams using proprietary stuff like RPGMaker). Look at me talking about what other people should go and do again, why don't they ever listen to my infinite wisdom and lack of personal effort.
I don't think making an acceptable pokémon AI would be all that hard... most trainers pick their moves nearly at random, and even at E4 levels in more recent games things don't go much beyond "which attack does the most damage to the current pokémon OR heal if in the red." Battle Tower's a bit better but not by a ton. Though, for what it's worth, I'm hoping to play with Technical Machine a bit in the future... I'd like to try and put it in a learning framework, so that rather than starting out knowing how to play well, it becomes better over time as it battles more against the player, which would hopefully allow for a much more challenging AI for people who want that kind of thing, while not being too daunting for people who kind of suck at the game, because then it would be learning based on a terrible teacher, so to speak. It would work perfectly with the plot of the FR/LG ROM hack I would like to make that would be, essentially, an AU to my fanfic--you don't even know the grandiose plans I have cooking for this thing, it is in fact ridiculous.
Oh, and you don't think there might be more than five people interested in battling with some random person's weird fakemon, or at least a particular subset of them, in the near future? As in, soon? SOON, right?? >|