Yes, but only after setting it up first.
Wyze Cam v3 is meant to work with an internet connection, which allows you to view the Live Stream, get notifications, and change your camera settings in the Wyze app.
You must have an internet connection to set up the camera and configure it with the Wyze app. And if you have a microSD card inserted and Local recording to microSD card turned on in your settings, the camera will continuously record to that microSD card, even if offline.
When your Wyze Cam is offline, you will not be able to connect to the camera via the Wyze app to view the live stream video or change any of the camera settings. The camera also will not save any alert videos to the cloud, so none of the motion or sound detection features will work.
To view your recorded footage, you can either bring your Wyze Cam back to an area that is covered by the WiFi network it was set up in and use the Playback feature in the Wyze app, or remove the microSD card from your Wyze Cam to view the raw video files (mp4 format) on a computer. When you return the microSD card to your Wyze Cam, it will resume continuous recording. The camera supports up to a 32GB microSD card, which holds roughly 2-3 days of playback recording. As it maxes out in space, it will overwrite the footage of the oldest day on file.
So while the camera can do offline recording, it is not its optimal purpose.