In 12.1, it will fall back by default, but not at once. See LU policy > Schedule > Options for skipping LiveUpdate. There is an option "LiveUpdate runs only if the client is disconnected from SEPM for more than x hours". You can use that to run a LiveUpdate schedule if the clients are not connected to the SEPM.
By default, LU schedule will be activated if SEPM cannot be reached for 8 hours AND AV/AS content is older than 2 days.