This is a very good question to me. You already have rolling blackouts. What happens when more and more convert to ev. This is the biggest hurdle in my opinion. Fire up the coal and gas plants?
I think in practice, if it really got that bad that here really is a natural disaster or demand surge that would cause electricity on the grid to be unavailable, there will also be a run on fuel as well; you are in the same boat as the EV owners.
You can just look at the recent Texas power outage as realworld example. People went and bought all the gasoline to run generators; and all the gas stations had huge lines and were out of fuel, so you couldn't get gas either.
Energy is somewhat convertable/interchangeable, so if the infrastructure is failing that much that there is not enough total energy (of any form) to meet the demand; you are not going to be protected from that infrastructure failures because you have an ICE vehicle.