Interesting question. For me, the question of whether or not someone possesses a mental illness or not has to do with the degree to which they can handle their mental issues. To a degree, mental issues (that sometimes get misclassified as illness) are natural, normal and also healthy to a degree too (your body/mind informing you of psychic/spiritual/psychological issues that require attention). Ignoring the mind/body's call to address such issues, hiding from them or running from them or ignoring them and allowing them to fester and get worse (or relying too heavily on drugs instead of also devoting attention to them and seeking the resolution) is evidence that one "can't handle it", and it is at this point that I myself would classify someone as possessing mental "illness". Bear in mind that the block can be unconscious in nature too, and that the person might not be aware of it.
Of course, there are cases of mental illness that are so severe that they can't really be solved anymore; although I think far more cases get classified this way than are actually the case. Severity of symptoms is not by itself proof that the illness is no longer curable.
I only bring all of this up because this is how I feel about mental illnesses and whether someone "has it" or not. In other words, I am asking myself to what extent I feel that A) Faith is aware of the underlying issues somehow (on whatever levels) and is trying to work out the underlying sources (in her own way, explicitly or not so much) and B) if she is getting by in life well enough despite it (in other words, is she "handling" it well). Expressed another way, are Faith's problems directly attributable to mental health, or only indirectly or not at all? If the former, I'd be inclined to say she has something, possibly ptsd; if the later, than I would say no, she has problems of the kind and nature that most of us have, despite her more unusual beginnings and behavior.