I'm somewhat doubtful. This would mean that the wii would have a totally separate partition of the internal flash storage of the size of the wii NAND (about 500MB, IIRC). While better on the safe side, it does limit things a bit. If you had bought more wiiware than you had internal storage, it would be disappointing that you still can't play all your games on the wiiU (there's a lot more storage, but it's reserved for wiiu games).
Access to an external HDD is, indeed, out of the question: you'll need to have a cIOS for that. And that can't be installed (yet?).
Oh, and for the record: the wii nor the wiiu doesn't have an internal HDD. It's called flash memory. I don't want to go anal over a name, but in this case, it's important that we're on the same page.