It depends on what is delivering power to your home at that time, home load, etc. Sometimes its unnoticeable, sometimes, there is a few milliseconds lag, which is enough for some computers, routers etc to reboot.
For example, if you have solar + powerwalls providing all of your power for your home load, you wont see any change. If you have all of your home load covered with just your solar and your powerwalls are on standby because they are full, you might see a blip in an outage as the solar turns off and the powerwalls turn "on" to power your home.
Basically, if your home is already being powered with some powerwall power, then you wont notice a change at all. If it ISNT (powerwalls being charged by solar, or in standby, etc) there are times when you will notice a blip.
Whether you want to cover for that "sometimes" depends on you, but there definitely is "sometimes" you will notice it without any UPS on computers / routers, etc.
Yep this is exactly the case. The outage hit when the house was pulling from the grid so there is a quick blip as it islands the house from the grid and flips to the batteries.
I have a few small Cyberpower ups units just for my Comcast router and my mesh wifi unit.
Also another tip I got from the forum is do a full Powerwall test to make sure the default 65hz signaling frequency they use to shutoff the inverter does not cause issues with your appliances. I had a few issues and Tesla dropped the signal frequency to 62hz which resolved the problems.