Are there any medical diagnosis systems that are already used somewhere that are based on artificial neural networks?
Yes, there are many, actually. A Google search turned this paper Artificial Neural Networks in Medical Diagnosis (2011) by Al-Shayea up.
Not only are they used in disease diagnosis, but even with things like prescribing medicines. In fact, the top project for a hackathon at my school analysed thousands of research articles, and took a patient's medication history as input, to best recommend them specific medicines. Check it out.