Yes, you need the chime connector if you mechanical doorbell is connected. Without the chime connector the doorbell is sending a constant low-voltage to the solenoid in the door bell and that is why it is buzzing. If you leave it connected like that then there is a good chance the solenoid will burn out. Until you resolve this I suggest you disconnect the wires going to the solenoid and that way your doorbell cam will continue to work.
