That is fine but it would be nice if the app does not rely on the system’s false flags if it is conenected or not. Maybe some kind of override would be nice for sure.
DAVx⁵ is a sync adapter and relies on the synchronization framework of Android. If Android thinks there is not internet connection, it won’t call DAVx⁵ for synchronization.
Please make sure that Android APIs work as documented on your phone; otherwise apps which use those APIs can’t work well. DAVx⁵ relies on working Android APIs, like many other apps. For instance, you won’t be able to receive emails or sync your Firefox data “without Internet connection” as well.
I suggest to change the captive portal URL to something on your own server and de-block the connectivity check in your firewall.
BTW, it’s called DAVx⁵ or DAVx5. Please don’t call it DavX.