No, the hat doesn't really enhance the outfit, kind of looks like an afterthought.
Actually I love the style of the hat. Quite Jackie O. The color could have been different but it look like [in another photo] that she was complementing her purse. As long as it wasn't one of those things that sit on forehead and zoom up in the air like a flag. Anyway, she looked brilliant and even perfect for a casual garden party.