Don't confuse Ubuntu or any other desktop feature-heavy distribution with Linux itself. I've ran linux fine on devices with less RAM than that.
Of course, since Linux is only the kernel used by Ubuntu. You probably could come up with a configuration that would run with the limited amount of memory on a Wii.
But would you want to? What features would you have and what software would run on the system?
There's a difference between can you and would you.
I could see using Linux on a Wii, but not for general computing. It would make a interesting media server/playback device.