It's very possible. Generally speaking, if it's connected to the web, it's vulnerable
It's probably more challanging though, does the Wii even have an OS? If not, whos to say the malicious users dont target the Wii, but target your router? If they have control over your router, then they pretty much own you
Ever heard of Drive By Pharming? It allows attackers to create a Web page that, simply when viewed, results in substantive configuration changes to your home broadband router or wireless access point. As a result, attackers gain complete control over the conduit by which you surf the Web, allowing them to direct you to sites they designed (no matter what Web address you direct your Web browser to).
And then theres the whole Wi-Fi part, depending on how Nintendo configured there system, it could be extremely easy for someone to capture packets, resulting in VC numbers, and other important data ^^