Before you sign this off as one of 'those' threads, the situation is a bit different. Instead of having a web-login, a username/password is actually required to connect to the network itself. Here's an example of what attempting to connect to the network on a PC looks like. So, is there any way to connect?
Yes, assuming you have a browser available on the WiiU to complete the authentication.
For all intent and purpose, the WiiU is simply connected to an unsecured WiFi connection. The router just redirects everything to the authentication page.