There are girls who begin developing earlier than their peers vulnerable to depression in adolescence.
Yes, I suppose that could be parsed in one of two ways:
There are girls who begin developing earlier than (their peers vulnerable to depression in adolescence).
or:
There are girls (who begin developing earlier than their peers) vulnerable to depression in adolescence.
In the first case, the sentence would seem to almost imply that depression might delay development. In the second case, it would seem to almost imply that early development could be the cause of the depression.
Both interpretations would be grammatical.
Other studies have shown this same pattern, with girls who begin developing earlier than their peers vulnerable to depression in adolescence.
Both meanings are possible when this phrase occurs after the word with as well.
However, there is a bit of a fallacy in your question:
Without context, are there two meanings?
Yes, without context, we could come up with two meanings. Thankfully, though, we usually do have context. Therefore, the study previously talked about presumably provides enough context that the intended meaning is apparent.
As a footnote, I'm guessing that it's the second meaning that applies: girls who develop early are vulnerable to depression.