There were four passengers on a recent WDH-JNB service, including myself and a friend. Our four bags were the first onto the carousel. YMMV and this is one data point, but it appears Comair do prioritize baggage.

With respect to LHR T5, do baggage handlers have no role at all? I get that once bags are put into the system, they'll get to the carousels when they get there, but surely feeding them into the system more quickly should result in them arriving at the baggage hall more quickly? I'm not sure why the level of automation would have anything to do with it... there's lots of airports with highly automated baggage systems that manage to process priority bags.