I'd say to start with, you need to define what you mean by 'God'. Are we talking exclusively about the Judaeo-Christian chap with a long white beard living in heaven? Or is this a wider context to include, for example, the Gods and Goddesses of the Hindus or the neo-Pagans?
If you're using the former definition, I would say to your question, no, absolutely not. If you're using the wider definition, I would say, no, probably not.
The use of the word 'spirituality' suggests the acceptance of the belief in spirit, i.e. something that goes beyond the merely physical. Does that 'something' imply that there must necessarily be a Divinity? Probably not. Buddhists, for example, might not believe that there is one head honcho God/dess, but that there is nevertheless a greater truth than we humans cannot comprehend without spiritual evolution. And some might say that we all have a spark of Divinity in us.
A really good question, Naomi, thanks for asking it. You've got me thinking.....