Absolutely, numerous studies have shown that the natural differences between men and women are minuscule. Apart from the obvious differences surrounding the sexual roles, all the observed differences between men and women are artificially created through gender conditioning. As such it is more than possible that anyone, no matter what their genetic makeup and what organs lie between their legs, can become a man or a woman and know exactly what that means and feels like. Being a man or a woman is little more than a state of mind and following a detailed set of rules and behavior.
The difficult part is that it is very hard, maybe impossible, to jettison all that you have learned since childhood to switch genders. If you were brought up as one gender as a child, that that experience will define who you are as an adult. But that does not mean that if you do decide to switch genders, your experience is any less real or relevant than that experienced by "genuine" men and women.
We are all trained to believe that the labels male and female mean something beyond the act of procreation. It is becoming increasingly evident that this is not the case, these are just labels for a job description which we are programmed to follow if we want acceptance from others.