If a girl goes through precocious puberty, will she go through menopause before 40?

Puberty. There are no studies i'm aware of that show an association between precocious puberty and early menopause.
Not necessarily. Puberty and menopause may not be related. For some people this may occur, but not everyone. It is more important to look at reasons as to why people start menopause early: stress, illness, weight changes, and genetics. Stay healthy, eat well and if you take care of yourself, health can be maintained easier.