Let's answer this question slowly: Would a person with Anorexia nervosa be more likely to break a bone than a regular person?
People with Anorexia Nervosa restrict food and as a result lack essential nutrients. Many people with Anorexia Nervosa, are at high risk for osteoporosis(and to a lesser extent bulimia nervosa) will have low bone density and consequently reduced bone strength. People with Anorexia Nervosa, are at high risk for osteoporosis. So the answer is yes.