Bought and downloading. :)
Is it possible to play the full game without Online mode?
Yep completely. There's a simple set of icons on the Forza Life menu where you can easily switch between online and offline.
One benefit of playing offline is that there's much more AI traffic making the world seem more alive. That'll change a bit when more people are online, but playing just now just had 24 people in my game. There is still AI traffic, but not as much. So I went offline and my world came to life.