I think Dawkins would say the role of religion is not to exist. That he would say that theism works against our interests more than it helps, so he would say no Christians understand the proper role of religion.
I'm not sure he would go that far. Remember that Dawkins is an evolutionary biologist, and to him, there is always an explanation for why some feature or trait persists in a species. I think Dawkins would more likely qualify your statement with "now that we have science, we no longer need religion." I've read some of his books and there's a sense that you can justify the existence of religion as a socio-evolutionary trait of humans. Our early society demanded something, an idea both simple and powerful, to germinate around. Something that promoted beneficial traits, like a strong sense of community, and not to ask too many questions, all while "explaining" the natural world. This was religion's role. Something which would promote the survival of one tribe over another, so that the most devout tribe was likely one of the strongest. But, now that we have science, logic, and rational thought, we no longer need religion as the very core of our societies. The social nature of humans is both well established and self-sustaining (barring global catastrophe, of course), and I believe his opinion would be that we're long overdue to jettison the booster-rocket of religion, and rely solely on science and logic to be our main engines from here on out. Pardon the rocket metaphor.
That's my take on him, anyways.