I think Mythbusters did an experiment on this previously.
Cant remember the exact details, but they hit something like 100 balls straight towards the branches of a tree to determine the chances of the ball sailing straight through.
Like Courteney says, the main "body" of the tree is not solid so there is always a chance that your shot will be completely unaffected!
On the flip side of that, I have experienced in this game before, where your ball hits a tree and bounces backwards down the fairway back towards the tee box!