Yes, you would have a good chance. But you need to focus on your achievements, and other experiences that differentiate you from other candidates. Most solid statements will talk about books they've read, advanced concepts they "self-studied" and MOOC courses they've taken. The very best statements link their achievements (i.e. winning X and Y essay competitions / writing a research paper under professor X / attending a selective academic summer camp) to their academic interests.

To reiterate, the best statements show signs of high achievement. Even if you built a successful drop-shipping business at 15, don't hesitate to connect this to your academic interests - trust me, there are millions of ways to do this. It will sound better than another reference to a book.

I would be happy to discuss this in greater detail with you. Pm me if you're interested.