400 w inverter isn't much power. I've had issues with battery powered inverters, the battery doesn't supply enough voltage to activate the inverter. 12-13.8 volts. the inverter I have only works if the voltage supplied is 13.8 and great, and I must run the vehicle to get it to work.

The solar panel would be good to keep the battery alive though, but will take a long time to recharge if the battery is really drained.

I made my own similar setup for Ham Radio use and emergency situations, but the battery always was dead or going bad when I needed to use it. The cost to replace it was significant and I never needed to use it. So I gave up on that item.

All that said, it might be good for the small dwelling use when there isn't much room for generators and similar items.