Wii U mode shouldn't affect vWii or vice versa when it updates.
Well, earlier, it did for me. Sort of. But only if your IOS's are messed up. Particularly IOS58. The problem was that I had a messed up IOS58 that I mistakenly updated with the Wii version beforehand, and when the Wii U update came up later, I got Error Code 162-0002, not letting me update, no matter how many times I tried. Leaving the update uninstallable, and eShop unaccessible, ect.
I had to actually go through a bunch of steps that the guys here helped me out on to go fix IOS58 and restore it to the proper vWii version of it. Suddenly, as soon as I did that, the Firmware Update worked like a charm. So, clearly, for me at least, it affected something.
However, the thing is, from what I can tell, I think the firmware update CHECKS the vWii system when it updates, even if it doesn't write or change anything. That's the only way I can explain how my screwed up IOS58 was getting in the way of the firmware update until I fixed it and then it immediately worked.
Now, I'm not 100% sure on that being exactly the case, as I don't exactly know the inner workings of what 4.02U does, but apparently, a discrepancy in the IOS was enough to tell it "Nope, you're not doin' this update." just based on what I can tell happened here.
Now this is speculation, but I have a theory about what caused my problem at the time. Before it installs the update it "prepares" the update. Maybe during that "preparation", it's just scanning to make sure everything is in place.
But I really don't think anyone should have the same problem as I did, anyway. My difficulty came about because I blatantly did something that was dumb and is advised not to do in the first place. I have a feeling that most people will be fine as long as they make sure NOT to do that. I don't think cIOS, or anything else should impede the update. Just a crucial, semi-brick that got in the way.