Critical micelle concentration (CMC) is a property of soap when it is diluted in enough water to make a "true" solution. CMC doesn't pertain to soap in a bar form.
I need to head to bed, but here is some stuff that may or may not be useful to you....
I tried to figure out what post that Susie was thinking of and the only one I can come up with is this:
http://www.soapmakingforum.com/showthread.php?t=46114 It doesn't specifically discuss using salt in bar soap, but it might give you some things to think about.
The post below is something else I wrote, but I apparently didn't share it anywhere. Or at least I can't find it here on SMF. Again, it's more about liquid soap and how it can be (sometimes) thickened with salt, but it may have some tidbits that apply to bar soap.
Here is the post -- with a few comments in brackets [ ] that I added tonight:
By adding a salt (table salt, sodium citrate, etc.) to a diluted liquid soap with the goal of thickening it, you are trying to reduce the solubility of the soap molecules in their dilution water. As you add more and more salt, some types of soap molecules are not able to remain dissolved in the salty water. If all goes as planned, the soap will eventually coalesce into small droplets floating around in a large body of salty water. At this point, the soap and salty water blend is an unusual type of mixture called a colloid. [If you do this same thing to an NaOH soap dissolved in water, the process of adding salt would cause the NaOH soap to separate from the salty water (brine) and form a layer of solid soap floating on the brine.]
What's so special about a colloid? If you've ever made hollandaise sauce, mayonnaise, or hand lotion, you know the individual components in the recipe -- the oils, water, etc. -- are pretty runny. But when you put the ingredients together and form a successful emulsion (aka a colloid), the ingredients magically become thick. When any mixture of two materials forms a colloid, whether it be eggs and lemon juice or soap and water, the viscosity (syrupyness) will increase. The proportions of the ingredients are important -- too much of any one ingredient can cause the colloid to "break" and the mixture will become thinner.
Getting back to soaps... Some soaps are only slightly soluble in a salt solution. To use a salt to thicken liquid soap, you ideally want to be working with a soap that is only slightly soluble in a salt solution. Some soaps are like this -- they would be the palmitic, stearic, oleic, linoleic, and linolenic soaps. Other soaps, such as lauric and myristic soaps, are highly soluble in salt solution. That is why it's tough to thicken a LS made with a high % of coconut, palm kernel, or babassu either by dilution alone or by using salt.
When you are making a batch of soap from any given fat or blend of fats, you get a mixture of different types of individual soaps -- lauric soap, myristic soap, stearic soap, oleic soap, etc. Each type of soap has a characteristic pattern of behavior related to the temperature and to the water content. Some soaps willingly form a colloid, others not so much. That's why it's confusing and difficult to find that "sweet spot" where the diluted soap is nicely viscous (syrupy).
The lauric and myristic soaps (from coconut oil) are highly soluble and disperse easily in water, even salty water. That is why bar soaps made with a high % of coconut or PKO are preferred for washing in salt water or cold water. [And this is why salting-out an NaOH soap made with coconut oil requires a LOT more salt than is needed to salt-out other types of NaOH soaps.] Lauric and myristic soaps, whether liquid (KOH) or bar (NaOH) soap, will go from a thick gel directly to a true solution with little or no syrupy sweet spot in the middle. It's difficult to add salt to this type of soap and get it to form a colloid that will stay reliably thick over time. These soaps are likely to need a separate thickener.
Oleic soap, on the other hand, is not as soluble in salt water AND it has a tendency to absorb a lot of water within its structure. This property of absorbing water while remaining more or less in a solid form is called "gelation capacity". When a high oleic fat is made into a liquid soap, this gelation capacity becomes an asset, because this type of LS is much more likely to form a stable, thick colloid over a wide range of water content.
The large gelation capacity of oleic soap is a disadvantage in a solid bar soap -- to many people, a bar soap made from olive oil and other high oleic fats feels "slimy" when wetted. The soap soaks up the water and swells but remains fairly solid. Think Jello gelatin made with less water than usual and you'll get the idea. This firm gel doesn't rub off nicely onto your skin or washcloth and it takes more work to get the soap to dissolve and form lather. Soaps lower in oleic acid soak up water and swell too, but the result is a soft "mush" (yes, that really is the technical term!) that rubs easily onto your washcloth or hands, dissolves quickly in water, and lathers easily.