Q: The core of both Bhagavan's and Swami's teachings seems to be, 'I am not the body or the mind. I am the Self'. It seems that all desires arise only because we identify with the body and the mind. From this it follows logically that if one could drop this habit one would automatically be in a desire less state. Is this true?

It is true. If one gives up the idea that one is the body and the mind, one is already living on a higher plane.