I promise you, your hair will not grow back darker or thicker. It is physiologically impossible. When the hair is removed it just grows back exactly as it was before, no darker, no thicker. The hair is removed from the surface of the face. The hair follicle remains in tact and the hair remaining in the follicle will just continue to grow, exactly as it is, no thicker and no darker.
Some people might have a few chin hairs that are a little thicker and, sometimes, darker. When this is removed, it will just grow back exactly as it was before. Dermaplaning will not change how the hair was originally before this facial.
There are two types of hair on your body. Firstly there is Vellous hair, which is the peach fuzz, very fine translucent blonde hair on your face. Secondly there is terminal hair which is a thicker coarser hair and grows on your legs, under your arms, eyebrows, beards for men. When terminal hair is cut it still grows back exactly as it did before, coarse, but it is more noticeable as the cut end is blunt and this is more noticeable when the hair is coarser, giving the impression that it is growing back thicker. It is not.