Would it help my client for her to stop talking to herself, and is that possible?

Stopping this is not in her best interest. It is the way she processes her thoughts, and doing it out loud, in a sense, creates a greater emphasis and certainty, whereas the thoughts within her mind are less precise and more susceptible to becoming distorted and influenced by emotion as they are being formed and therefore less reliable in helping her to sort things out. So this, for her, is actually a helpful coping mechanism. It is not that she achieves perfection and has well-balanced and rational healthy perspectives on all matters. She has many deep inner fears still, and many areas of concern in her life, many yearnings, and unfulfilled desires, and still much naïveté and the state of ignorance about many aspects of life she has yet to experience, all of which keep her at a disadvantage. The quirkiness of her behavior does work against her as well, and that is certainly a downside of this behavior, but it is inherently not dangerous and is not readily suppressed, as evidenced by her inability to do so despite great encouragement.