I have no idea what happened to my Wii months ago when I moved but I shrugged it off because I was planning to get a Wii U. I just ordered a wii u and wanted to know if anyone had any luck with nintendo support to reinstate your purchases on a new system without having the original wii console available. I have about a dozen VC purchases and a free copy of mario 64 from club nintendo.
You won't know unless you call Nintendo. They could answer this question prior to purchasing a Wii U.
Purchases are tied to the Wii in question. If you have the Wii's serial #, then there's a chance the purchases can be restored. I've once found myself with a bricked Wii due to a power surge, and Nintendo required the serial # of both the old and new Wii in order to do the transfer.
I was unable to find any information online about whether or not you need to have the Wii in question, nor can I find anything that says they no longer do this. In that regard I would give them a call and let them be the final answer.