It depends. Most wireless doorbell cameras typically require a Wi-Fi connection to function effectively. Wi-Fi allows the doorbell camera to connect to your home network and transmit data, such as video footage and alerts, to your smartphone or other devices.
However, PoE doorbell cameras do not necessarily need Wi-Fi for their primary functions. POE cameras receive both power and data through an Ethernet cable connected to a POE switch or injector.
If you use Reolink doorbell cameras without an Internet connection, the doorbell camera can still detect motion/person and record videos to the SD card. However, it cannot send alerts to your mobile devices, and you cannot live view it.
If the chime is connected to the doorbell, it will chime when the doorbell is pressed, regardless of the Internet connection.