The answer is yes. Being a hypochondriac can be exhausting. You spend all your time worrying about having a serious medical illness, and this gives you anxiety. Because you have constant anxiety, this sets off your fight or flight response, so you then become hyperaroused, which requires a lot of energy. After a while, you become exhausted. In addition, you become even more tired after you visit with multiple doctors and receive multiple medical tests in search of a diagnosis that your doctors tell you that you don't have.