it wont read it..
that disc will have been made for a standard cd/dvd rom drive (ie in a pc) so the drivers on there will be for the pc only, plus the wii reads discs from the outside-in, so it most likely wouldnt be able to read it anyways..
an update wont sort it, the update needs to be downloaded, how would they expect you to download an update to allow you to connect? it doesnt make sense..
you would need to get a replacement adapter. i noticed you got yours from newegg, thats one of the places i read alot of people had compatability issues with them adapters