LiveView adds a `phx-disconnected` class, which is what I assumed you mean by beachball, and interactions are paused while the user awaits the UI to tell them they are good. This is all driven by your CSS and you can also hook into the connection life-cycle with a few lines of JS, so the app should be telling the user "Reconnecting..." vs it appearing broken, so this is really up to your UX folks. By default new phx apps make use of the topbar library so any page loading event or dropped connection will show the loading bar/spinner up top.
As far as spotty connections go, when I try simulating 30% packet loss, my LiveView WebSocket connections have no perceptible degradation, so it's hard to say where the cut off is. You can also fall back to long-polling which may benefit very edge users, but I would only do so if absolutely necessary.
Having said all that, one thing we are upfront about in general is LiveView is obviously not a good fit applications that require offline support :)