N00b Question about Wired Eero

So we are fortunate to have ethernet ports in most rooms in our house. However, because our "master panel" and router are located in our closet in the rear of the house, we get spotty wireless coverage in the front end. I now have a new Eero6 plugged into the port in the front room which shows up in the app as "Gateway eero". My question is, do I even need an Eero plugged directly into my router in this case (which I currently do)?