OK, I now have no idea what you want…
Again…
If Blynk IS NOT connected, then as long as your programming is setup to keep running without that link (see here for an example), then you should be able do whatever you want with the modem… attempt reconnection to Blynk, ET phone home, answer spam calls, whatever…
If, however, Blynk IS connected, then generally that is ALL the modem (or any other method of link, WiFi, USB, BT/BLE) can do (maintain that connection), and thus unable to do anything else.
Perhaps a little more clarity of your “problem” 