I haven't tested this myself, and I don't know if the people in the videos use action replay or not. But, this question (answered by redring345) has an answer and a couple links to videos.
In short, yes, you can. It's called Missingno, the generic glitch Pokemon throughout the generations.
Calling it a "programming quirk", Nintendo warned against encountering it, claiming players could possibly have to restart the game from the beginning to remove the graphical glitches ... a potentially game-ruining glitch.
So, that's from the Wikipedia. Bulbapedia says basically the same thing. Your graphics could become scrambled and you may have to restart the game in order to fix it (or at least, that's how it was in the first generation of Pokemon; like previously stated, I do not know the effects for the 5th Generation).
