I don't think so... I think of at least the big 4 religions (which are based on the soul) there could be no way of believing in god without it.
The reason why I ask is because I think it is FAR more likely that humanity will be able to PROVE that when we die NOTHING happens. Then we could ever prove that there is an invisible creator.
We are learning so much about the brain. We may even be able to transfer our consciousness to a synthetic brain within our lifetime. We may be able to simulate death entirely.
I think religion needs souls..
Many ancient religions did not have doctrines regarding eternal life for the common person. In the ancient Egyptian religions, for instance, only the Pharaoh had an afterlife - and perhaps obedient servants would be a part of that but not necessarily.
I think of religion as an evolving cognitive virus. The major religions we have today are here because they burrow so deeply into the psyche and propagate so easily. The major drawback to a religion not promoting a soul doctrine in today's world would be how unappealing it would seem compared to the religions that do offer that option.
Actually, Heather, even the Old Testament didn't recognize any likelihood of an afterlife until quite late in the book.