If you design it correctly yes.
If you have a dc coupled hybrid inverter, it is a given that you can use the solar panels to charge the batteries.
If you have an AC coupled inverter, you may not be able to start charging the batteries, that's where the devil is in the details. Something needs to trigger the AC current to charge. AFAIK, the newer equipment is more likely to do do this like the newer Enphase product line compared to the older stuff. I guess the newest Tesla powerwall has an option for off grid.
If you are using 1 mWh/ month, you still need to plan the outage to be on the peak month. My summer months use 6 times the electricity of the winter months.