If you have OCD as a child, are you at risk for developing anorexia as an adult?

Yes, but... Although there is an association with childhood OCD and anorexia nervosa, most people with OCD do not develop anorexia nervosa. Anorexia nervosa is, itself, a serious illness with inherent obsessive-compulsive features, so there is considerable symptom overlap between anorexia nervosa and ocd. Anorexia nervosa is a life-threatening illness and anyone who may have it needs immediate evaluation.
No. No, there are not scientific studies directly linking OCD with anorexia.