Due to a GAF thread a good many years ago I did try the whole not using any soaps or shampoos for about half a year or so. It was OK, but not great. Even when I resorted to using Apple Cider Vinegar to wash my hair every few days my hair still felt way too greasy and dirty after just a day or two. My skin too was OK, but it didn't feel much better or anything. It wasn't a total failure, but it wasn't exactly a worthwhile alternative.
Before then I used to go overboard with soap and exfoliating every day and I had pretty dry skin as a result. I would often take two full showers a day scrubbing everything thoroughly. And using moisturizing soaps and lotion never seemed to alleviate things and it always made me feel greasy and uncomfortable afterwards, negating my thorough scrubbing altogether.