Strictly speaking, yes. Atheism just implies a lack of belief in God or gods. Buddhists are atheists, many of whom believe in reincarnation. Such people would be spiritual in your sense. You can find other variations, though they're rare. Usually, belief in gods comes bundled with a belief in the soul.
Most people who call themselves atheists are also scientific materialists who don't believe any mind-body duality or other supernatural ideas. So in this sense, the answer is closer to "no".
Finally, there is a feeling of spirituality or connectedness with the natural world that I think is a human trait that everyone can feel regardless of their beliefs. That doesn't seem to be the sense you mean.
--Don