To clarify Frisky's post. You can use the Hard Drive on the new Wii U, but you will have to formatt it again. You won't be able to transfer or use the data from the first Wii U once that is done. After formatting on the new Wii U, you would have to formatt it again to use it on the first Wii U.
So if all you want to do is continue to use your Hard Drive without buying a new one, and don't mind losing your saves and game installs, then go ahead. Just make sure to go into system settings and reformatt that hard drive on the new Wii U.