Iwata: To go back a little further, the Nintendo GameCube system actually had 3D-compatible circuitry built in.

Itoi: Huh?

Iwata: It had the potential for such functions.

Itoi: Nintendo GameCube did? And all the Nintendo GameCubes systems around the world?

Iwata: Yeah. If you fit it with a certain accessory, it could display 3D images.

Itoi: What a secret!

Iwata: Nintendo GameCube was released in 2001, exactly ten years ago. We’d been thinking about 3D for a long time even back then.

Itoi: Why didn’t anyone ever know?

Iwata: The liquid crystal for it was still expensive. Simply put, Nintendo GameCube could display 3D images if you attached a special LCD, but that special liquid crystal was really expensive back then.

Itoi: Yeah, we’re talking about ten years ago.

Iwata: We couldn’t have done it without selling it for a price far above that of the Nintendo GameCube system, itself! We already had a game for it, though—Luigi’s Mansion, simultaneously released with Nintendo GameCube.
This is from a recent 'Iwata Asks' interview. So since the circuitry is already built into the GC, would it technically be possible to mod it so could output 3D on a 3D screen? I could certainly see someone from the modding community trying this.

Although I guess if it is, it might be pointless due to a lack of 3D games?