Yes, the firmware in the lock should allow the Privacy to work that way if the lock is toggled.
If you toggle CO lock with the privacy function, when you close the door and push the button it will go into privacy, locking out the reader and locks the door. When someone egresses the lock or pushes the inside button again, the lock will come out of privacy. The reader will return to the normal state and the door will go back into an unlocked state.
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