If by "undercarriage" you're referring to your delicate parts, the answer is no, especially for the vagina and anal areas.
Harsh soaps can cause drying, cracking and itching, and should be avoided. In fact, it's best to minimize the use of soap at all: just a little water is enough. If you do use dr. Bronners, make sure and follow his instructions: "dilute! dilute! dilute!".