I knew someone who never used soap on their body because of a medical condition and their skin would react. Suffice to say they didn't smell like BO, but they did have a heavy sweaty smell to them like after a workout. Not pleasant.

Water alone will do nothing to body oils. They just stick. Bacteria then start to digest it and you get a smell.

Overall, water might cut down some of the smell, but without soap, you're going to smell sweaty.