Should have used GTAIV or Fable II as an example. Obviously you can if Fable II has sucky multiplayer and it is all mission co-op, or look there is 100% offline games (Just Cause 2) obviously it will be playable offline.
That's not what he's asking.
Yes, after you download and patch the game it is on your HDD, so you can play it without being connected, as far as I know.