No. You can get pure glycerin and I assure you it doesn't lather at all on its own. They also make tripple milled soaps which have most of the glycerin removed and they are considered a premium product by many. It's the surfactant part of the soap that lathers (or foams depending on the oil/fat used). The combination of fats and oil used to make the soap determine how it lathers, with a small effect from additives (scents, moisturizers, etc.).
Also it takes LYE (Sodium Hydroxide) to break down and combine the oils and fats giving them there saponification value. Now, there are others oils and fats you can add to make a more stable lather instead of bubbles like Cottonseed Oil just to name one. Glycerin will just give your lather a slicker feel on the skin.
I would agree with this... isn't it tallow and other relative ingredients that make the lather??? I have some glycerin based soaps like mama bear and QED that actually have more of a gelatin feel and don't really lather up in the bowl. They do well with boar bristle in my experience and will lather up as it's applied to the skin. It does tend to have more of a adhesive gel feel as opposed to fluffy lather.
