Good question, @Monkeyfloor .
It's not a yes / no answer though, as it's more about whether smart meters are the dominant system or not, and whether you're rich or poor.
In a system without smart meters, energy rationing is usually done through "brown-outs": rolling power cuts which affect whole districts at set times. So every one gets a chance to charge their phones, do their cooking, cool their freezer back down, etc.
In a system where most households had smart meters, rationing would be done by surge-pricing: temporarily increasing the price until sufficient people switched off most of their lights/heating/appliances, bringing down the total load.
Of course as with all systems where scarce resources are allocated purely by money, Lord & Lady Moneybags would still have their outdoor swimming pool being heated, while Mr & Ms At-Their-Gates would be sitting round a candle bundled up in their coats.
So if you're rich, you're likely to be a winner under smart meters: everyone else will turn off their appliances so you can keep yours on.
Smart meters and surge-pricing also have political advantages. Brown-outs are an actual Thing; they can be pointed to as an obvious failure by government to provide critical national infrastructure.
Whereas pricing power out of the reach of ordinary folk is merely a failure by poor people to be rich and virtuous. Politicians would wax lyrical that feckless parents were choosing beer and gel nails over keeping their children warm and fed. We could write the headlines now...