I was recently asked this question. The response came from a Buddhist practitioner. This was my answer:
The difficulty in answering the question is that it depends on the definition ’spiritual’. Since Buddhism is an atheistic religion, the same could be asked of Buddhism. There is probably a large consensus among people that Buddhists are Spiritual People but an equally large consensus may also believe A-Theists are Not-Spiritual People. The duality is unnecessary. I would argue that efforts to connect mind-body (ie..yoga and meditation) are spiritual practices with or sans belief in a Patriarchal Deity.
Two words: Carl Sagan
One word: Orgasm
Lots of people said they are Atheist, when the time come (disease, illness, dying), they always become lost and looking for spiritual support.
The question that we shall ask is can an Atheist now be real Atheist later ?