The USB ports aren't even active (not the same as powered) unless the Wii firmware is expecting input through them, so I doubt it
Technically, they are active during the Internet channel with the new firmware that allows USB keyboard to work.
So, if you could make an exploit allowing access via Internet channel, it could work.
But there poses the question: "Do you need to break the Wii encryption".
I can think of 100s of dodgy keyboard presses that would cause the Wii to flip out and start loading isos through it.
...
Actually, I can't.
A keyboard driver is too simple to even be exploited. Really, all it needs to do is listen to the device on the USB port, and if the bit patterns being sent through they port translate to characters, then print them on the screen.