Well, GRBL is open source, so I imagine you could stack an ethernet shield under your motor driver shield and add ethernet support to GRBL. I suspect there’s not enough space for it, and not enough spare compute power to keep up either. One of the newer Arduinos with more memory and more horsepower might well be needed to do it well. You could probably use WiFi as well, albeit with an even bigger memory footprint.
Have you considered just running an amplified USB cable instead? I’ve worked on projects where we extended USB and DVI to 30 metres or so.