It depends on how fully it emulates a wii and what restrictions it would have, but I'd say if the thing quacks and functions like a wii (you have support for the controllers, the disk drive, network things, etc.) it could be called a wii

This strikes at the root of the Biggest Controversy™ - if you beat a video game arcade cabinet on an emulator, did you beat it?

Things can be named analogously - if I have a machine that plays Wii games for me, and nothing else, I'll call it "the Wii".