Can you share your computer's wireless connection and then try to connect your thunderbolt? I still don't understand what you would want to do with your Thunderbolt's connection that you can't do on your computer, unless you're wanting to download and play with online Apps. I'd personally rather use my computer to do surfing and online gaming.
The biggest factor is if your computer can share the internet connection that it's using and whether or not the Thunderbolt will see that as an actual connection. Also you can connect the Thunderbolt to a computer that's online and there's an option to use the computer's internet connection, but you'll probably have to configure the computer to allow for the connection.