It's possible. Nintendo did it as a marketing scandal. There's a few things you need, (homebrew channel, a custom one with 16:9/full screen, a application called wiilauncher, I'll get the links later). Use wiilauncher, go into config setup hook none, switch aspect ratio to 16:9, save config, and launch channel once you leave config.
here is the tutorial bit, so first your going to need yawmm which is right here https://sites.google.com/site/completesg/how-to-use/wad-manager make sure you get the one with vwii support it will say it!!!! next is http://www.hacksden.com/showthread.php/7814-Workaround-for-the-HBC-with-the-latest-Wii-U-update this is the download page for the custom hb channel with fullscreen support, choose your colors, you got dark blue, black and yellow... is that.. ok anyways once you have those files put yawmm in apps folder if you don't have one create one. it needs to look like this when you open your sd card (you can have extra stuff but I mean make sure it exist this way) (apps) (YAWMM_EN) and somestuff within that. ok once you checked that is place properly, get your other file (it should be a .wad) and put it on the root of your sd, aka when you open your sd card in a file explorer and haven't moved into any other folders. last but not lest you need wiilauncher (sorry i don't have a good enough rep since i Just joined look it up, it should be in wiibrew . org or something like that when looking in applications, it description should be a alternative to gecko os (gecko os is a cheat manager thing, but i found out that using wiilauncher without cheats allows it to be run in fullscreen) ). Ok do the same with with wii launcher like yawmm. Ok get your sd card in your wii u run the homebrew channel, run yawmm, and install your .wad file, this is why I said root because its just easy to find it, once that is installed leave yawmm and leave the homebrew channel, you should see a new channel, which is the color you choose, use that homebrew channel, now at last, run wiilauncher, I recommend you change your config, the reason why is so if you do have cheat codes (somehow) it won't run them which is why putting the hook type to no hook (disables cheat codes in its entirety) and set the aspect ratio to 16:9 aka fullscreen. and launch channel. I must tell you this trick might not work for certain vc, such as sonic the hedgehog, but super mario world, mario kart 64 super mario 64 (just a lot) wil work, note this is for wiiu in vwii mode