The present invention relates generally to a manner by which to page an access terminal of a radio communication system to alert the access terminal of a pending call, or other communication. More particularly, the present invention relates to apparatus, and an associated method, that provides for the generation, sending, and analysis of a quick page message upon a paging channel, such as a QPCH (quick paging channel) defined in an exemplary cellular communication system. The page message is formed in a manner that reduces the likelihood of occurrence of false wakeup of an access terminal. Excessive battery depletion, as a result of false wakeup of the access terminal, is avoided.