No. Gecko OS does not run burned wii games. It lets you run games from other regions.
http://wiibrew.org/wiki/GeckoOS
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no with the wii you can only play wii and Gamecube games
Yes, you can play nintendo wii games online.
No it is IMPOSSIBLE to play DS games on the Wii but you can play Nintendo Gamecube games with the Gamecube controller
Go to the wii shop channel and you can buy them to play on your wii.
You cannot play Wii games on any Nintendo DS system.