Yes, if you cut off all the bleached hair, the new hair that grows in will be your natural, original color. Bleaching only affects the hair that's already been grown out of your scalp. It doesn't change the color of the hair follicles themselves.
Think of it like this: hair is dead. Bleach changes the color of the dead hair. Your hair follicles are alive and produce new hair with your natural pigment. Once the bleached hair is gone, only the new, naturally colored hair will be visible.
