Internet is not required to watch your Slingbox over your home network.
Once everything is set up it'll work fine. For any computers connected to your router- by ethernet or Wifi- your Slingbox will show up automatically in the SlingPlayer Directory. You can watch from there.
If you ever need to run Setup Assistant, no internet might make things a slight bit more difficult to set up. It can be done though- stick with your desktop SlingPlayer software and you should be fine. It's got what you need to run Setup built in.
If your Slingbox is already up and running, it doesn't need the internet for local viewing on your home network.
Hope this helps !