Chevy Volt according to Wikipedia has something like 16.5 kWh.
I don't know how big your house/flat is and for how much power your AC unit is rated for, but it should be enough for at least 3-5 hours under a full load for a rather powerful multi split AC unit.
If you keep in mind that AC doesn't draw full power to keep an already cool room cool, your car might be just enough to keep the AC running through the night or majority of daylight hours.
The smarter move would be during an emergency to get everybody into the Volt and let it cool that smaller space. It won’t be as comfortable, but the battery would likely get you through the whole night at a decent temperature.
"This advice doesn't apply in all situations and the commenter didn't disclaim this in their comment so I'm going to be sarcastic about the situations where it doesn't apply so I can be right and feel good about myself"
A quick Google search says a central A/C unit takes about 3 kilowatts to run. The Volt has a 16 kWH battery, about 11 usable, so you'd get a few hours out of a charge.
That said, the Volt is a hybrid. Its battery is relatively small because you're carrying a gas engine and can go farther if you need it. My Bolt's battery isn't huge compared to some cars coming out, and its battery is about 65 kWH. Should be enough to power a house for about a day, and it only gets better from there.
Biggest use-case for this is during extended power incidents where you need to keep your fridge cold, run fans during hot days, and allow for hot meal prep if you have a plug-in burner.