Can the Ring Spotlight Cam Plus Plug-In recharge an installed battery?

If the Ring [Spotlight Cam Plus Plug-in](https://ring.com/products/spotlight-cam-plus-plug-in) has a [backup battery](https://ring.com/products/quick-release-battery-pack) installed, will the battery recharge inside the camera when line power is available? Context: The outlet I intend to use with the Spotlight cam is controlled by a timer, so my plan was for the camera to be powered by line powered when the timer was on, and battery when the timer is off. But this is really only an acceptable solution if the batteries get recharged inside the camera when line power is delivered.