How do the limited timed games on Steam works? For example, I downloaded Saint's Row on Steam which is free for 2 days. If I finished the download on the first day, will my game be unplayable on the dead line even though it's on my computer?
Pretty much. Or more precisely, if you try to start it after the free period passes, steam will attempt to authenticate that you own the game, realize that you don't, and refuse to start the game.
I don't think it deletes the data, mind - after all, it's in their best interest to make it as easy as possible for you to decide to buy the game - but until and unless you actually buy the game it's just taking up several gigabytes of space on your hard drive.