There are a couple of elements brought out in the question that require some examination. The first is that the idea of being a representative of the people is rooted in the basic notion of being democratically elected. It is from here where the wellspring of representative government flows freely. Without this component, there cannot be any right to hold office because the consent of the governed has not been sought or given. In this, I think that the second half of the question is resolved in that there can be no right to a democratically elected office or government unless there has been the consent of the governed given through voting and direct election. However, "self- proclaimed" an individual might claim to be, this, by itself, is not an automatic entitlement to office. Some might argue that even being democratically elected does not entitle anyone to office. Serving at the behest of the people through representative democracy is not an entitlement of any kind and no elected representative possesses a natural right to hold any kind of office as the people possess the right to recall their elected officials and hold them accountable. In this configuration, a non- elected individual has no sense of direct political power in a representative setting.