No. In the event of a power outage, services that rely on the internet will be disrupted (i.e. CCTV, back to base alarms etc.)
During a power outage, you will be unable to make or receive any phone calls, which also includes contacting emergency services.
For further information please visit https://www.nbnco.com.au/learn/network-technology/fibre-to-the-premises-explained-fttp/battery-back-up-information