I think it's dubious. There's nothing about soap that will shape the edge qualities. As you said, it's about friction between blade and stone. I'd only ever heard of soapy water (don't know if you meant this and not straight liquid soap) on oilstones, but this is the first I've heard of that for waterstones. Most all (I suppose I can't say 100%) users continue to use water and get excellent results. I would think the thicker your liquid media, the less quick your results, as friction is more dampened.
The stone slurry you build that really does the cutting. Many people wash that away as they sharpen shortening the lives of their stones. That's what a nagura is for - to build the slurry before sharpening. Soap is usually used as a lubricant, but with Japanese water stones water is the lubricant.