No. SmackDown vs. Raw 2010 released on PS2, PS3, PSP, Xbox 360, Wii, DS. Not on GameCube.
If playing on Wii (backward compatible or Wii version): Plug GCN Controller into GameCube Controller Ports (Top/Flap) → Works natively.
If on Wii U: Needs Wii U GameCube Controller Adapter (Smash 4) + GCN Controller.