As already said,Get a battery air pump. Just to be safe.
Im about to use an inverter for a car(its a electrical box with household plugs in it) and wire it to a car battery. Mine provides 600watts of power. So i should be fine in case a power outage happens. Best part is I can run my lights and my pumps, and skimmer pump too!
Fwiw, the best way to aereate water is by photosythesis( using plants in the tank to produce it) So having some lights on will be good.
But in your case with corals, I would think that flow is more important. Because they need to remove the respirated things that surround their skin(zoox) outer membrane. Without flow corals die, espcially sps.