Yes. Not all systems are the same, but many of them come with a built-in battery backup so that they will continue to monitor your supply line and activate their safety measures if a leak sensor detects an issue during a power outage. Although they do often use a nearby power outlet as their main source of electricity, that battery backup will activate in the case of a power outage. Be sure to carefully read the features of your chosen system and choose one with a battery backup for the maximum level of protection.