Good Question: Simple Answer. No.
No. At Least, not yet. And the reason: The SD Card slot is missing. And that’s more crucial than you think. The Wii only reads from the SD Card, not from the USB Port. Though the Wii Mini has a USB Port (only one though), it’s sole purpose is to mock the hacking community that it can’t be hacked. As I’ve mentioned in my last post, Smash Stack only works the SD Card. This is because the USB ports are completely obsolete and Smash Stack can only be loaded from the game’s compatability with the SD card. And since USB port support isn’t implemented in SSBB, You can’t use it. Another flaw with this is that the USB port is connected to the internal hardware, but is not coded in the software to actually do anything. Which is where The Homebrew Channel comes in. It adds a patch which allows homebrew software to read from the USB port.
Until someone is clever enough, there isn’t a way so far. sorry =(