If you run @thebearmay 's Hub Information Driver v3 ([RELEASE] Hub Information Driver v3) it can show when the hub has lost cloud connectivity. You could build a rule to turn on / flash a light when that attribute goes to 'disconnected'. From what you posted, it sounds like sending a notification to the mobile app wouldn't work while the cloud is disconnected, but you might be able to send a notification by other means (Pushover, email to SMS, etc).
As far as NTP and DNS, I've found that when I lose cloud connectivity, I'm not losing all network connectivity. I set up a flow on Node Red that calls http://hubitat.home.lan/hub2/hubData every 5 minutes and notifies me if the data returned shows the cloud is disconnected. That process has been working, so even when the cloud is disconnected, that endpoint is still responding on the LAN. I assume (but could be wrong) that NTP and DNS would still be working also.
In addition to the monitoring via Node Red, I've set up a rule that reboots the hub if the cloud shows disconnected, as reboots have been fixing the issue for me.
