I’ve used mine during short power outages with no issues. How long the NBN side equipment will run for during a power outage will depend on which technology is used. For FTTP everything is passive between the house and the OLT in the NBN POI. The NBN POIs generally have large battery backups and generators so can run for a long time.

For FTTN, there is a VDSL DSLAM in the street cabinets that requires power and I believe they have some battery backup but I’m not sure for how long.

FTTC uses a small DSLAM in the pit outside of the house (1 shares between 4 houses) and these are reverse powered from the house so if the house still has power (e.g. the NTD is on a UPS) then I believe they will keep on working.

I don’t know much about how the HFC network is built but I think there is active equipment in the streets that has limited battery backup.