Apparatus, and an associated method, by which to page a mobile station to alert the mobile station of a call placed thereto. A location server is provided at which a location index is created and maintained, identifying the location at which the mobile station to which the call is to be terminated is positioned. Page messages are broadcast throughout an area in which the mobile station is indicated to be positioned. The page messages are broadcast in manners that permit the mobile station to detect their transmission even when the mobile station is in a dormant, or other nonactive, state.