Not sure I understand completely, but here is my experience.

Most of my ‘older’ speakers run off of SonosNet, by connecting to a BOOST that I’ve set up nearish my router. My Era 300s, on the other hand, are ‘bonded’ to my Arc, and as a result, get the IP address they use from the router, but the WiFi connection from my Arc. The initial setup of those Era 300s used the same signal (WiFi) that my Roam and Arcs do, until they were bonded. To my knowledge, the Era 300 can not connect to a SonosNet signal, as they don’t have that electronic capability. 

By the way, your PLAY:1s are ‘bonded’ to your Arc, just like mine were, and are receiving their signal from the Arc, not hanging off of SonosNet. 

It is unlikely your system is even using SonosNet currently as Sonos products that are used as home theater surrounds or subwoofers are unable to act as the first-wired product for SonosNet.

Era 300 also does not support SonosNet.

There is one other thing that is not recommended by Sonos, and that is, having a Sub or surround be the main device connected to your network:

https://support.sonos.com/en-us/article/switch-sonos-between-a-wireless-and-wired-setup
 

Read the “Home Theater “ section.

So as others have said, your system is not using SonosNet and the Arc is the main speaker that the Play 1 is connected to,

That being said, if you were to replace toe Play 1s with Era300s, you will not need to worry about connecting them to your router. They will work without the Ethernet cable.

Thanks. So are you guys saying I can ditch the Ethernet connection and the speakers around my home will still work with the app and music streaming?

As long as you put your WiFi details in your controller before you disconnect, it should.

Make sure you read the Sonos Network Requirements FAQ first. 

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