Mentioning resolved illness to statement of purpose?
I wouldn't put it in writing as it is too easy to misinterpret. If someone thinks that the condition might return it won't work in your favor. Other people have situations that make it hard to study also, medical and otherwise. 

I would be less concerned with mentioning it in an interview if it would be a natural part of the conversation, but even then, will require explanation and possible misinterpretation.

Represent yourself as a hard worker who gets things done and performs at a high level. The rest is unimportant.