Well, I tried all of this, and researched a bit, here is what I have to write about:
First off, vWii (at least, in American units) is native 480p despite the Wii U progressive resolution (480p, 720p, and 1080p, all of them have a 480p vWii, not 480i like a user suggested, I didn't test 1080i).
I know this thanks to Settings Editor by JoostinOnline, when the app boots, it shows the current config of your Wii, mine was at 480p in all modes that were tested, I tried to force my vWii resolution to 576i, but it seems that Americans vWiis can only do 480i as interlaced, because it will turn into 480i when I apply the setting.
Now, I took some photos to compare all of this, first from 480p upscaled to 1080p, then 480i upscaled to 1080p, and last native 480p.
https://drive.google.com/file/d/1nV1CE-iJep9ARRke4y9WU20srUFI5_rK/view
https://drive.google.com/file/d/15BZ6pOX9qVUTYiwI2yw1JXJ8FnIftkmy/view
https://drive.google.com/file/d/1wKGsiSpv1BlNxSka-iuqtoBmraQaY4op/view
In these 3 photos you can see the differences, I know they are not very good, but I do notice the difference, so I think is enough.
Do zoom, and check the part where the finger is pressing the A button, you can notice that the first one is upscaled to 1080p, it's crisp compared to the other 2, however, it is more jagged too, the native 480p one and the 480i to 1080p image looks blurrier thus the jaggies are camouflaged.
https://drive.google.com/file/d/1wx-4hT1gjvXM8wVNPxdCgJZ8t2deiYxM/view
https://drive.google.com/file/d/1tWaNYhA-4Z4IdwgAqyGWb-zqxRytnbZW/view
https://drive.google.com/file/d/1ggFQi5vCQmxki1nRonb8S1Kp3Pm7DS1n/view
In this image you can see that the 480pto1080p is still the crisper, the 480ito1080p is the blurrier, but has less jaggies, and the native 480p is between these two in sharpness.
So... I can say that native 480p or upscaled to 1080p has differences, the first one is less sharp and blurrier, also the colors are a little bit less powerful (just like the original Wii), but the upscaled one has slighty better colors, and it's a lot sharper, the image looks clearer but that means jaggies are more noticeable too, also some artifacts appears that are unnoticed on 480p. It's a matter of likes, native 480p looks like the Wii.
Here is a last photo, upscaled 480p to 1080p, vs native 480p:
https://drive.google.com/file/d/1dNMDBMNGqXOCbH2kSSQj40nR69Zs5cd7/view
https://drive.google.com/file/d/1a2X-I686NI1tqXsHvOO4TE8SNBrmhsgj/view
In my taste, I prefer the first one, it has more jaggies, but I just prefer the colours and sharpness.
And about the upscaling the TV does... I think that the Wii U surpasses a TV, at least on my case, native 480p on my TV is just a 480p expanded to my whole screen, it looks ultra blurry, in another TV that is smaller than this native 480p looks a lot better, but it's 55" vs 27"...
So, it's a matter of likes really, what it looks better is up to you.
Going to the first message of the topic, everything in software is possible, you just need to do it, in this case, you need to know how vWii communicates with the upscaler... maybe the vWii grabs the Wii U mode resolution? Maybe the vWii doesn't do anything and the Wii U just enter Wii Mode like if it where another software? In this last case, I know the Wii U treates the Wii Mode in a special manner, it disables some cores, and also locks cache, and downs the clock speed of the CPU, along other changes, but what I mean is that maybe the resolution that you set up in the Wii U config is universal for everything (games, apps, etc), so in this case modifying the vWii wouldn't help.
I don't really know how this works, but I think this case is the latter, but it's only my speculation.
Anyway, 480p in the end of the day is 480p, it doesn't really look good unless you have a CRT or a small TV.
Even in small TVs it looks OK, not awesome, it's called "Standard Definition" after all.
What would be awesome is to have a Wii Hybrid Hardware-Software Emulator though, but it would be a hassle to do, the idea would be the Espresso CPU runs the Wii software natively, and then the GPU7/GX2 emulates the Hollywood to do 720p/1080p native res, as far as I know, the Wii U doesn't have the entire Wii GPU but components that let's do it thing.
But that's utopia, it's not going to happend.