If you have any amount of energy storage then the time delay doesn't matter. You turn on the alternate generation method when the storage is starting to run down. It doesn't matter if it takes an hour to come up to temperature because you still have two hours of storage left.

The actual problem is that "shortfall" is a relative concept. Do you have to burn coal because it's cloudy all week, or just because you spent a lot of resources building coal-fired power plants instead of solar panels or wind turbines or nuclear reactors? How often are you going to run the things?

The economics of building and maintaining an entire fleet of coal power plants to use only in a demand emergency is extremely poor. Like you're better off spending half the money on nuclear reactors you can run 100% of the time and the other half on electrifying transportation so you can have a huge demand buffer in the form of vehicle batteries and then get people who only drive a few miles per day to delay their charging by a few days through pricing because a full charge lasts them three weeks anyway.