RN-->NP here applying to med school. In a word, no, don't shadow us if you actually want to be a physician. I agree with those who have said above that shadowing nurses to differentiate our role(s) from that of a physician's role is a GREAT way to learn more about healthcare and the different disciplines you would work closely with as a physician. But the work of a bedside nurse is nothing like the work of a physician. And the work of an NP is highly variable based on practice setting.
NP or PA work may *look* like physician work on the surface, but the difference in level of responsibility for patient care is vastly different (with the physician having much more responsibility). So, while it might be good exposure to patient care and the clinical setting and even some of the day-to-day routine, which can overlap between physicians and mid-levels, it's not a good way to determine if being a physician is right for you.