The simple answer is no. The Roku devices need an active internet connection to stream content. (they can't "borrow" the internet connection from your ethernet connected tv.) As such, the Roku devices need either a wireless (wifi) or ethernet (wired) connection to a network. (Or at the least, an external HDMI switch with ethernet port).
The more complicated answer is that there was the ability of some roku devices (Streaming Sticks included) prior to Roku OS updates that were able to stream LAN (network) content without an active internet connection, but seems currently limited to Roku devices that are ethernet connected (Ultra and such). Caveat here is that you must set them up on an active internet network before using them on a non-active internet network.
If you are needing an ethernet capable Roku streaming device, you can look at the Roku Ultra (ethernet ready) or the Express 4k/4k+ models (ethernet adapter purchased seperately). If you want to use a Streaming Stick, then you will need wireless capability.(wifi)
Roku Community Streaming Expert Just another Roku user... I am not a Roku employee. Insignia RokuTV, Ultra 4660, Premiere+ 3921, Express 4k+ 3941, Streambar 9102
So if I have a smart TV that comes with roku and I connect an ethernet cable from my router/modem to the ethernet port on the TV then I am actually connecting to the Roku in the TV,, Right?
Just want to know because I am purchasing a new smart TV that (unlike my other smart TV) does not come with roku and I want to hardwire it for streaming rather than use wi-fi. Even though my new smart TV has an ethernet port I would still need to purchase the roku device that accepts an ethernet cable (Ultra and such) and connect my ethernet cable to the roku device and then the roku device to the TV,, Right?