Thecatmilton...a mini-USB is just a USB connecter. The internet is just a world wide networking service. The two would need a multitude of help to communicate directly.
For instance, you would need a mini-USB compatible modem to interface your device with in order to get an internet signal. Then your device would need the proper hardware to support the modem. Also you would need the proper software to communicate with. Finally you would need the proper drivers to make the modem work.
So many variable to your question that need refining. For instance...
1. What type of device are you going to use, a netbook, computer, cellphone, etc?
2. What is the source of your internet, wireless, wired ethernet, Activesync connection, 3G, dialup etc?
3. What is the operating system on your device, Windows x86, Windows CE, Android, other?
But unless the planetary alignment is just perfect as it will be on Dec 21, 2012...the answer is probably NO!
Only thing I've ever heard about the internet through USB is using PDAnet on your phone to tether to your computer with the mini USB. So, if you have an Android phone like the one I'm using to type this, then yes. And the computer has getting the internet has to be a USB host, the mini USB being in the phone. But what are you trying to do, get the internet on a Sig III with a USB cable? If you can do that, you're a computer engineer. 
