Without installing a battery backup system with a grid disconnect switch, the short answer is “nearly for sure not.”
Behind the meter, the vast majority of solar panel installations are connected, meaning they feed power first into the house and to the grid if the house doesn’t need power. The grid is down when there is a blackout, and your system is designed to shut down automatically to protect workers who may need to repair lines connected to your home.
Nonetheless, if you have mounted the battery backup or taken other measures to keep the solar panels running during a power outage, you may have enough energy to keep your lights on.