Atheists helping a church? Would a church let them?

For a while now I have wanted to be able to allow broaden the people who are able to serve on different committees of the church. For instance, I would love to have an atheist or an agnostic on an Evangelism team. I have no idea if that would ever be possible because generally atheists are not interested in helping churches. 

But really I think a sell that would be just as difficult to do is to convince the church to allow an atheist or agnostic or even a non-member to serve in different areas of the church.

All of this comes out of a renegotiation that I really have no idea how to engage non-Christians in religious conversations. I have no connection to the atheist community or even really understand all the arguments against organized religion. I get that organized religion has a history that is bloody - but all of humanity has a history of blood. I get that parts of organized religion provoke hate even today, there are also a large number of organized religions that provoke love. I get there are some intellectual arguments against the logic of the existence of a deity and yet I understand that most of Christianity is not logical at all (love neighbor, die to self, non-reciprocal altruism, turn the other cheek, violence is never good, etc.). 

I would love to have non-religious in our church to help build bridges. I only wonder which would be the harder group to convince - the non-members or the members?