Here's why:
* Colosseum is a Generation 3 game: It features Pokemon from generations 1-3, with a focus on the Hoenn region. Pikachu is from the Kanto region (Generation 1).
* No direct trading: While you can trade Pokemon with other players using the GameCube's link cable, there's no way to trade with players of the original Pokemon games (Red, Blue, Yellow, Gold, Silver, or Crystal).
Therefore, obtaining Pikachu in Pokemon Colosseum is impossible.