Hmmmm. Sounds rather dangerous, no? I'd imagine you could easily catch some type of bug/virus that can corrupt your save data or crash your game. You're right, it kinda does defeat the purpose of the game. Which was mainly built around trading with friends or meeting new people to trade with. Has this site been approved by Nintendo? Or does it not matter since it's not breaking any license agreements?
tl;dr but I hope this makes sense.
Not really, DS games aren't able to experience that kind of problem. I can't exactly explain why as I'm not a tech whiz, but DS games can't receive viruses like computers and phones can. While you can download glitchy looking Pokemon, they can't necessarily corrupt your save file. In addition, you download glitchy Pokemon by your own choice as the site has something called a Legality Analysis which outlines things like the trash bytes contained in the name of the Pokemon and the OT and also other hidden variables that can be used to identify its legality.
But in short, no, you cannot get a virus of any sort, but yes, you can download glitch Pokemon which I assume can turn into Bad Eggs in your save.
Also while it does defeat the whole original purpose Satoshi Tajiri intended Pokemon for, there are positive uses. As EV has mentioned, you can use it to transfer Pokemon from Gen IV to Gen V with only one DS which is a good thing for people who do not own a second one. Another benefit being hack checking, as I've mentioned, Pokecheck can identify hidden variables that point out its legality.
Other benefits being able to check your Pokemon's exact IVs, a way to catalog your Pokemon, keep back ups in case you misplace your game. Dunno if I can name anymore than that at the moment.
And it hasn't been approved by Nintendo for various reasons. One probably being that there are some people who do indeed use it for cheating and thus spoiling the point of the game. But I'd imagine it does follow fair use in some way as it doesn't affect sales of the game from what I know and it the owners and creators don't use it for making money either.