We think so, because 'awe' or 'aww', in the context you describe, often is said when a young woman, or any woman for that matter, is overcome by adorable cuteness. This often comes in response to hearing something sweet, affectionate or flattering being uttered, or seeing something adorable (like new puppies or kittens).
Aww is often an expression of sympathy as well, in other contexts. So if you had an accident and fell off a bike, she might say "aww" too.
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