Yes, as a basic doorbell.
If Wyze Video Doorbell does not have an internet connection, it would no longer send push notifications to your phone. You also wouldn't be able to access the doorbell in the Wyze app or view the Live Stream.
The connection to Wyze Chime is local, and doesn't require internet. If someone rings your doorbell, you will still hear the chime as long as both devices have power.