I do believe it is possible for an atheist to be spiritual. Buddhism is an atheist religion and I would describe them as being very spiritual. But a lot of that also depends on what your definition of 'spiritual' is. Theists tend to believe in spirituality as ones soul and their direct connection to the souls of others and god. Where as an atheist might view spirituality as one's connection to the universe, being a series of molecules that contributes to an incredible whole.
I'm also still surprised by how few religious people understand where atheists find strength for morality and growth. It's a misconception that some sort of deity is required for us to act civilized. Yet from an atheist point of view, it's confusing that someone who has a great deal of personal strength and morality would, for some reason, give credit to a mythological being, rather than themselves.