In both cases, either surround use or as a separate room use, the Amp would connect wirelessly to the Arc. The Arc still needs to be connected to the TV to receive either eARC or ARC, via HDMI,

Thank you so much, everything sounds amazing - Sonos AMP with Sonance 4 ceiling speakers. Sonos ARC connected to Sony A8h and Sonos Sub. The only caveat is the ARC needs to be connected to Ethernet - it doesn’t allow over WiFi if you are trying to connect it for a home theater. The Sonos wouldnt group the sub and amp with the arc without Ethernet and true play never setup properly.  

Odd. Both of my Arcs are connected to WiFi. Granted, I use PLAY;1s for surrounds. 

Yeah I get it. In the Sonos S1 app it could see the ARC on WiFi - the WiFi is 10 ft away so connection is strong. The AMP, the sub are on WiFi - but when you try to group everything in one profile the wizard shows you need to connect an Ethernet to the ARC. Otherwise True play wouldn’t complete and then the sound would only go through the ARC only. Once I connected Ethernet the true play completed and sound was amazing - just a little odd.

Are you using a Sonos Amp or the older Connect:Amp?  The Connect:Amp would require an wired connection between Arc and Connect:Amp, but the Sonos Amp shouldn’t.

Edit:  And unless I’m mistaken, the Arc can’t be controlled via Sonos S1.

Apologies S2 app - Sonos AMP. The Arc is connected to the Sony a8h by eArc. The amp just has the four speakers attached.

The Amp should connect via a 5Ghz signal from the Arc then, assuming there’s no wifi interference , and the distance isn’t too far for a signal to reach.  I’m not sure why you’d be getting any “need to connect by ethernet” message, that seems odd. I’d be awfully tempted to refresh both the network and the Sonos devices by unplugging all Sonos devices from power (all of them), then rebooting the router while they’re unplugged. Once the router comes back up, plug back in all Sonos devices.

Basically reloading all the software on all devices. Because that message makes no sense to me, and it should “just work”. Unless there’s some sort of interference causing the Amp not to connect to the Arc. I guess I’m repeating myself because it really is contrary to the way it is supposed to work.