I do this everyday on the client side (taking my laptop to work, opening the lid and having my session going on), and sometime on the server side as well.
Using the thunderbolt Ethernet helps.
Edit: just read parent's reply talking about RDP
* One port dedicated to a monitor * The second has to do double duty, swapping between ethernet ports and another monitor as needed.
I also have a USB->DVI adapter (https://www.engadget.com/2013/05/11/kensington-usb-3-0-multi...) when I need both the monitor and the ethernet port, but it's crappy. (Flickering cursor, occasionally cutting out, some applications like IntelliJ and Sublime Text have issues rendering on that monitor)
That could then go in a USB hub, which my Apple display includes.
(I haven't tried this.)