To let the screen work correctly, it needs to be online when it is connected to the system. Also for synchronisation of the playlist, the hardware needs to be online.
If you however lose the internet connection during playing, the playlist will continue to play. When you turn the screen off and on again without internet connection, it will automatically start the last played playlist. Because widgets get information from an internet source, it can be that the widgets display old content when the hardware is offline. It is also possible that the widget is shown empty (there is no text or image that is shown) when using it offline.