I think @bryonhu has done a lot with this type of stuff. You might want to take a look at the following and/or do related searches in the Forum:
For that model (Cam v3) and other “wired” (no internal battery) cameras, yes. After ~30 minutes without an Internet connection the camera will reboot in order to try to refresh/re-establish a network connection and after the restart will poll for time. When the camera finds that NTP is unavailable (because there’s no Internet connection), it will write the sequential microSD recordings using the firmware’s build date/time as the starting point. If your router can provide a constant Wi-Fi connection (even if it’s not connected to the Internet) and is capable of intercepting NTP and responding to requests, then you should be able to mitigate the problem, which seems to be firmware dependent (i.e., some older Cam v3 firmware versions aren’t affected). That’s my understanding, anyway. A post like this might shed more light:
Like @spkc notes, I wouldn’t expect Cam Outdoor v2 to have this problem with Travel Mode enabled, so that’s a good point. 
I don’t have any hands-on experience with those, though, and my understanding with continuous recording in the Cam Outdoors is that it has to be scheduled in the app and doesn’t just work all the time like when regular continuous microSD recording gets set for other Wyze Cams, so that might be less than ideal.
Also, I’m not trying to push Cam v4. I just think that it might represent a better feature value than Cam v3 (but I don’t have any of that model, and there are community members who seem to swear by them). The comment earlier in this topic about subscriptions being a requirement for Cam v4 is not factually accurate any more than it is for other Wyze Cams, though, so I wouldn’t rule out that model based on that one notion.
That makes more sense, in a way. When you set Event Recording in the app (at least for Cam v4; I don’t have any Cam v3s to test, so I’d appreciate any correction), I believe “Other Motion” tagging is permanently enabled (to make it easier to find in the recording timeline) but notifications can be unchecked, if that’s a concern. The problem with using this sort of motion detection without a subscription, though, is that it’s all based on changes to pixels in the images that the camera is collecting from moment to moment, so I can see how you’d end up with a ton of motion events in that scenario. Depending on your needs and what you really want to detect or capture, a subscription might make sense (but then again you’d need a reliable Internet connection that can upload to Wyze’s servers for the detection analysis).
It seems to be now, anyway. Until fairly recently, it was a vertically-scrolling timeline, which I liked since my oldest is a Cam Pan v3 and had that UI. This new one is yet another change, and I’m not sure if Wyze is just messing with the users or actually working toward a more consistent UI. I didn’t like this new development at first because it was unfamiliar (then again, so was the vertical timeline when I began using that), but it’s growing on me and seems to snap to events more reliably than the previous “new UI” did. I’m getting used to it and starting to like it more.