Apparatus, and an associated method, for a receiving station, such as the receive part of a mobile station, that has diversity antennas. The receiving station includes both legacy demodulators and a diversity demodulator. Calculations are made to determine signal indicia associated with the signal energy detected at the diversity antennas. Responsive to the signal indicia, selection is made as to whether to utilize demodulation data, demodulated pursuant to a diversity demodulation technique or pursuant to a legacy demodulation technique. As the characteristics of received signals change, reselection of the demodulation is correspondingly made, such as on a frame-by-frame basis of frame-formatted data.