question - do the representatives and elected members of a democracy rule?
Rule, under the definition of control or dominion, is "The exercise of authority over a region or people, or the duration of a monarch's reign (e.g., colonial rule)", the word rule is often applied to mean what the leaders of a democracy do, but in most cases rule seems too strict if taking the normative definition, thus there is an informal usage that applies to democratic leadership.
The President is often referred to as a ruler, corporate elites are often referred to as rulers; in these informal groups of rulers I think it is reasonable to place the Catholic Church.
I am agreeable to say they do not rule, but then we must admit they exert a great influence, in many places and ways greater than the governments that officially hold power.