The pump continues pumping and providing basal insulin regardless whether it is talking to a phone (or PDM if your pump has one).
If your pump has no UI on it, you will not be able to give yourself a bolus without using the smart phone app or PDM.
I am not sure whether it is the same for all pumps, but if my phone fails completely (not just switched off), I need to do a pump change to use the PDM instead as the pump is connected (via Bluetooth) to the phone app.
I always carry a syringe and my vial of insulin so I can handle this without a pump change when out. It has never happened.