The whole system depends, on how many panels you have, and that can depend on the battery and inverter you are using.
The are trying to get you to work out what is essential to keep running, so those will be powered in the event of a power outage. Remember solar panels dont work at night so no charging.
The more appliances you want to run will mean more panels, more batteries and bigger inverter. Could they hook up the house to the inverter?? Yes they could, but it may be at the inverter limit, and it will drain the batteries quickly.
Aircon at night will be a big load.