...mmmYeah, that's a big fat no. My system is officially an online-brick.
Called today. In case anyone out there is having this same problem, just call Nintendo now: 1-800-255-3700. Do it as soon as you can, save yourself the headache, since you won't be able to transfer save data from your old Wii to the new, even via SD card. Apparently, as idiotic as it seems, save games are tied to your Wii, just like VC downloads and the like. So, I'm going to lose about 10 hours of playtime in Zelda, my Miis and my Wii Sports data. Honestly, I'd be really upset if I were losing my SSBB data or something else that takes 100s of hours of playtime. This brings up the issue, what if you upgrade your Wii once a new color is released? Do you lose all of your data? That'd suck. Maybe there'll be a workaround for it by then, but who knows.
If you want to keep your data, you have to ship your system to them for repair. But I'm impatient, and I hadn't played that much anyways, so... Advanced System Replacement method FTW.