It appears that after your iPad is set up (I don't remember the steps involved to set up), I can say with 100% certainty that the iPad client does not need the internet to stream. However, the program guide of course won't work without access to the Internet. In your case, with even a modest Internet connection, the guide should work, as that is not demanding a lot of data.
So despite what you may hear otherwise from support, it is very easy to test this. Turn off your cable modem or disconnect the link between the router and cable modem. You'll see that for extended periods of time (5 or 10 minutes--I haven't tried longer, but that proves the point), the iPad client will continue streaming. The very nice thing about the iPad design is that it doesn't require the Internet to START the stream either, unlike the browser desktop client, which doesn't need the Internet to stream but DOES need the Internet to start/locate the slingbox since the URL is a slingbox.com address. That means the browser, once started, will not have its stream interrupted by Internet issues as long as the stream has already started for a LAN to LAN session.
From a common sense perspective, for the technically inclined, where would the stream go on the Internet? It is certainly not going to go to the Sling company servers, just to send back to the client, which would mean Sling would be paying for expensive bandwidth in BOTH directions for every single active slingbox connection in the world. For that, we would be paying sling media a monthly fee for the service, and that would be a big point of failure and additional source of problems for customers.