Nintendo crammed the Wii’s OS into the Wii U. So it makes sense that homebrew would still work on the new console. Numerous users have reported that it functions successfully on Wii U, mainly through a Super Smash Bros. Brawl workaround.
Also worth noting, homebrew content doesn’t affect Wii to Wii U transfers. The process shouldn’t encounter any issues, but, of course, all homebrew items will remain on the original Wii.