Sure, it could. However, you'd have to have reasonable expectations regarding what you can do with it. Compiling will be slow and swappy, for instance, but it'd certainly work.
USB 2 is more than fine for storage and ethernet. You wouldn't have the fastest nor the most efficient system, but if you're the kind of person who appreciates things outside of the mainstream, it'd make for an interesting server :)
No, I'm actually serious about this. Many projects like Wii-Linux exist and it would be great to take advantage of that to repurpose a Wii into a headless server.
USB 2 is more than fine for storage and ethernet. You wouldn't have the fastest nor the most efficient system, but if you're the kind of person who appreciates things outside of the mainstream, it'd make for an interesting server :)