Dizzy,
Good question. I don't know about the Alexander Technique, but I do know that in the theory of Neural Linguistic Programming, or NLP, they talk about modeling behaviours. So, if you see someone confident like you want to be, and you model their behaviour, you will start to feel confident too.
It seems to me that our minds and bodies share a two-way street. We know without doubt that our minds can affect our bodies, so it seems reasonable to assume that our bodies can affect our minds.
I read about a study recently that suggests that our stomachs directly influence our thinking, or are a part of the process. So if there is something wrong with your stomach, it can affect your thinking. Maybe that's what is meant by 'gut feeling'.
Even through this Role Transition that is bringing on anxiety, I find that if I stand tall, keep clean and well shaven, I have a bit more confidence that I will make it through. So, yeah, I guess I do believe that the body can affect the mind.