There might be a connection. If a woman is gorgeous, she just might be thinking, "Do people like me because of who I am, or because of what I look like?" She may be despondent over the dishonest intentions of men.
Depression isn't selective. Doesn't matter what we look like or how much money or social status we have. Look at Robin Williams. He was a millionaire. Well, he's dead, isn't he? He was totally depressed.
There's no relation.
Depression is a mental illness and does not discriminate - it can affect anyone. Young, old, rich, poor, man, woman. It doesn't matter how talented, loved, successful or beautiful you are. Anyone is vulnerable.