There are a few different Zone Systems on the market today , so, we'd really need to know which you have ...and, if you have multiple thermostats that control a respective duct supply damper , etc... Assuming you have a room thermostat controlling a room duct supply damper...the Bypass Damper you described would start to open up IF alot of the room duct supply dampers were throttling closed due to a load load condition ; in this case, the Bypass Damper would allow the airflow to purposely "short-circuit" and dump back into the return air duct. IN this type of Zone System, the Bypass Damper would be normally closed and pressure buildup inside the duct would open it .
If you dont have the type of Zoned System ive just described, then please disregard. But, to answer your question...no, the Bypass Damper should not be continuously open all the time under any condition.