I have never heard of this happening. Wii's can be "softmodded" which means someone manipulated the wii's operating system in such as way that it will allow programs to be installed on the wii that allow playing non-original discs on the wii. Nintendo has sometimes included software in their games that try to reverse this manipulation. New Super Mario Bros Wii is one game that I heard does this. It MAY be possible that a wii can get broken when the game tries to reverse the softmod, but most times it will just revert the wii back to a wii that doesn't play burnt discs. The other possibility it that there is a "mod-chip" installed in the Wii that allows it to play burned cds. A game like Super Mario Bros. Wii may notice that you have one of these chips and shut down the system (possibly permanently).
In summary, The only "viruses" or programs that could do harm to a modified wii that I know of are ones put out by Nintendo to thwart piracy.

P.S. I am no means an expert on Wii or Wii modification. I just read a lot! :P