Yes, quantum theory, although incredibly accurate, only gives the probability that 'events' will happen. But in order for La Place's demon to work, you have to assume that he would know all of the laws of the universe, and I think it's fairly certain to say that humans don't know all of the laws of the universe at this point. I think (conjecture) that quantum theory will be explained further. With that being said, (and this only being a thought experiment) I think it's at least worth conceiving that the idea of a unifying theory might be possible.
So, I guess the question would be; If a unifying theory is possible, could La Place's demon work?