Will no one be able to make phone calls if the entire mobile phone network fails during extreme thunderstorms or severe weather?

If there were an extreme storm, such as a thunderstorm, where there was no reception but the cell phone tower was undamaged, would all network users be affected? Because there are still priority contracts for e.g. fire departments, DRK, offices, etc. Would they then also no longer be able to make phone calls or would…