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