Except you'd have to segregate your solar system. That's kind of the issue with using solar as a "world goes to shit" system. It has to tie into your house, which means it ties into the grid. That is, unless you invest heavily in batteries. That's why people are always bummed out when they find out that in a blackout, their solar system essentially shuts off so it doesn't send electricity up grid.
I'm also not sure you can do that without a battery. My system (in our van) has the inverter connected to the battery, with a separate connection to the MPPT charge controller. Branching off the charge controller are the panels and a 12v fuse box. It's hard to explain and I have a crazy diagram I drew when I was planning it. I'm definitely not an expert though. Seems like you might fry your inverter with the power fluctuations though.