Every system behaves slightly differently. Your likely best approach would be to do a couple of grid outage simulations and see how everything in your home behaves.
Be sure to try when your Powerwalls are full (97%+) and your PV is producing more than the house is consuming, then throw the main breaker from the grid. When the grid goes down in this situation excess PV power has nowhere to go and it takes the Powerwalls + Gateway the longest amount of time to transition out of all of the grid outage scenarios.
Personally I have 4 UPSes in the house for all of my sensitive electronics: PC, security cameras and the NVR, home automation server, networking equipment (I use Unifi), and the family room TV + Xbox. It's probably overkill but I had them from before I got the Powerwall