The game creators would never allow that because they simply would never allow evil to win.
Of course, the definition of "Evil" is... not really fixed, so people could debate for days on end about the evil of Team *insert(magma:aqua:rocket:cipher:whatever)*.
I agree, this would be really interesting, receiving orders from Giovanni, stealing stuff, but the game tries to teach you moral lessons, and stealing isn't really a moral thing to do in most cases. Even though the game is too subtle for the lessons to be completely visible, they are present nonetheless. It would be against the principle of the game and it's rudimentary, underlying basis: discovery, communication, persistance, good from bad, right from wrong. An opportunity to join Team Rocket is not usually considered to contain one of those ethical meanings.
Au contraire, it teaches exactly the opposite of that. So, no. You cannot join, and you will never be able to join, even though, in certain aspects, it would be appealing.
Blastoise King said:
who the hell wants to train with those weaklings all day waiting for someone to come up a bridge? sounds like the most boring game ever if you ask me
Right. It would take quite a lot of programming and graphical designing in order not to make it boring.