No, scheduling is not supported. Android doesn’t provide the API for that. It could not only be done by a CalDAV synchronizier like DAVx⁵, but would require interaction with the calendar app etc.
I want to use mitmproxy to inspect DAVDroid’s traffic easily, but instead I have to install its custom certificate and use transparent mode.
From a quick Google search it doesn’t seem that this library does that automatically.
I have just tried out with DAVdroid 0.6.9.2 and a HTTP proxy in WiFi settings and it worked out of the box.
If this doesn’t work for you, please give detailled steps to reproduce and provide logs.
Since 897ede75821cf8028c46e16a10368053bb32070e, there’s even SNI support for proxied connections.
I tried with 0.6.9.1 yesterday and it didn’t work. Tried today with 0.6.9.2 and it did, so sorry for the noise. I probably made a mistake somewhere though (regardless of the version).