Use of a power inverter with my 2013 Volt

I want to use my Volt to power an 1100 watt power inverter in case of prolonged electricity outage. Is the 12v battery in the trunk strong enough for discharge from a power inverter? The manual recommends using a marine battery. When the battery is discharged, will the big battery charge the little battery? Do I have to keep the ignition on for this to happen? If the big battery gets exhausted, will the gas generator automatically fire up to recharge it? Does anyone have experience using such a setup? Thanks.