SunnyBoy has a "Secure Power Supply" feature that basically provides one outlet on the inverter that is powered even if the grid is out.
As others have said, if you want to power your whole house (or a significant portion thereof) you need something fancier plus a transfer switch to disconnect from the grid. It turns out the Powerwall is one of the cheaper options for the capacity it provides if that's what you're going to do. Also the transfer switch in the Gateway is pretty fast - almost fast enough for all equipment to stay up when an outage hits.