No, hair is basically protein and keratin and has no blood supply or nervous system. Your body does not know that your hair is cut because it has no way of communicating this information to your body. People often believe that shaving causes the beard to grow faster or thicker, but facial hair typically grows thicker and faster as you age so if you grow more hair due to shaving, it is likely only a coincidence. Hair styling habits don’t create permanent hair loss because they typically don’t damage the root of hair follicles underneath the scalp’s surface.
Getting frequent haircuts is a good way to keep existing hair healthy by removing damaged, split ends, but haircuts have no effect on your hair’s growth rate or thickness.