CCC can run backup tasks while the system is running on battery power, but will not (by default) start automated tasks when your laptop is running on battery power. Backup tasks generate a lot of disk read and write activity, and that can run your battery down. Additionally, macOS tends to aggressively put the system to sleep when it's on battery power, causing task completion to be deferred until the system is awoken. For the best performance of your backup tasks and your battery, we recommend running your backup tasks when the system is attached to an AC power supply.
Can I configure CCC to start automated tasks when the system is running on battery power?
Yes. Click the Preferences button in CCC's toolbar to access settings related to running tasks while on battery power.