No, you don’t have to pair the fitness HR strap. It features a wireless broadcasted emission (which is different from the Pocket Mate). Once triggered by your heart beat, the Fitness HR strap send the your heart rate to any device in proximity area. Once your device is connected, other devices will not be able to connect the Fitness HR strap as every connection is unique and coded.
That why it’s important, when connecting the HR strap to the app (before going for a ride or a run), you must be far enough away from the others (at least 20~30 m) to avoid interference and connection problems during connection.