Yes it is possible. (Score 1)

I was working as a musician before I decided to settle down and "grow up". I had only a diploma in music as a qualification. I have now worked my way up to Senior Developer with a great little company. I think that from my experience some companies are impressed by people who are self taught. It shows you have discipline to sit and learn unaided. My experience of developers who are straight out of University is that they may know lots of theory but ask them to complete a real world job quickly and they struggle.