The Wii U includes a way to transfer all your Wii settings (it requires an SD card and an Internet connection), and many Wii homebrew users have been concerned that the transfer might require a system update that would wipe out their homebrew. But one brave NeoGAF member reports that the Wii to Wii U transfer works fine with a homebrewed Wii. Apparently the important thing is that the shopping channel is updated, something the user did with DOP-Shop, (although I always use Pimp My Wii to keep things up to date).
The Wii to Wii U transfer moves your save games and other information to the Wii U, then deletes that information from the Wii. For those who want to keep their Wii settings intact, NeoGAF posters suggest doing a NAND backup (the Wii's uses NAND flash memory for internal storage), perform the settings transfer, and then restore your NAND.
While this won't transfer your homebrew, it is apparently possible to use homebrew on the Wii channel of the Wii U using the Smash Bros. Brawl's Smash Stack exploit. There is no way at present to install the Homebrew Channel on the Wii U.
I HAVEN'T TRIED ANY OF THIS. I am not making any promises. I'm not sure I'm even going to bother, myself, since I'm perfectly content to keep using my Wii for Wii games. But this is what I've read.