It is possible to receive the satellite internet data from some satellites. Capturing the files to your hard drive. Though I'm not sure of the legality of doing so, as I see it its illegal, however the fact that some services are unencrypted and broadcast via satellite could be interpreted as acceptable just like watching an FTA tv channel really.
Also you obviously have no control over what you are receiving. Which is pointless because you may as well go and look around the web yourself.