Yes. The main reason is that the stress response releases a bunch of hormones, specifically cortisol and adrenaline, which cause the fight-or-flight response. A side effect of this is that the body turns off (or at least, slows down) a lot of the functions it uses to take care of itself such as the immune system and digestive system. When this happens constantly over a long period, it can absolutely cause problems because your body is constantly trying to prepare to run away from some predator instead of taking care of itself.