Yes, deadlines are important for success, because they give people a reason to get their work done. If there were no deadlines, much of the economy would not happen, or it would happen poorly. Deadlines are important for students, because students have to be prepared for the real world, where they are expected to get their work done in a timely fashion.
In a perfect world, we could operate without the existence of deadlines. Unfortunately, deadlines are a very practical thing. They set a theoretical 'finish line' in our minds that we strive to achieve, and when we draw closer to that finish line, our effort is multiplied. Deadlines are a very useful thing, and should not be overlooked.