Technically it does not, but if the controller's workload is high, it may be the difference between being granted the service or not. Also, I believe they have ways to tag the primary return "blip" so the data stay with it. Just expect to be given some identification turns ("Cessna 123, turn 30 degrees left for radar idenification...Cessna 123, radar contact, resume own navigation") when starting the proces or being handed off (just like we did in the days before nearly all light planes had transponders).