Yes they can help but my experience shows that TD works better. Bentonite clay is great to add to shaving soap for slip. Because clays draw out impurities in our skin, be careful because they can cause a soap to be too drying for some.
Not sure if they would make a soap white or not, but the bentonite clay is more of a gray color. And the clays are more commonly used in shaving soaps for slip.
But also note that benonite clay is best for those with oily skin because they dry out the skin. So if your customer had dry skin they might not be very happy at all.
And kaoline clay is a more white color and is great for those with normal or sensitive skin tones. And is more or less ok for anyone to use.
I use a fine bentonite clay powder. It does not turn the soap any unsusual color - the clay itself is gray, but you can still color the soap whatever you want. It does draw out impurities and provide great slip for shaving soap, but I have seen people use it in any kind of soap. It can dry the skin a little, which is why I superfat my bars that have clay in them. I use 1 Tbsp. of clay per pound of soap. A great place to get it at a good price is www.bulkherbstore.com