Actually yes! You need to set your Wii U's resolution to 480p in the Settings, then boot to Wii Mode. Issue fixed! There's also another way that's a bit more complicated but is way faster: if your TV has a zoom-in mode, you can calibrate it that way, while still keeping 1080p.

Honestly on my TV so much of the screen is filled that I can barely notice the borders on Wii U vWii.