If your RUT is in the Wired WAN mode, i believe the LTE modem sleeps, so it would be unable to test to see if the internet is working over LTE.
You could however have an alert emailed when the LTE modem goes active due to the Wired WAN failing.
But if both the Wired WAN and LTE have no internet connection, how would the unit communicate...? If you're out of credit for example, it wouldnt be able to send an sms either...
Quite difficult to understand you're post and what you're actually asking.