Huh, so she can interact with the real world, and so far is only invisible to Hattori (we haven't gotten confirmation other people can see her).
So it's an unconscious manifestation of psychic abilities? Because a real doppelganger is supposed to kill you as soon as you meet each other, and if it was some other supernatural being it'd be weird if she looked like Hattori and capable of reading her mind, yet only decided to do something about her desires now.
I know I thinking about it too hard, but I like doing thinking exercises.