NixOS disk consumption is really bad unless you're going to keep it very minimal. On top of that, rebuilding takes a lot of computational power and RAM, so it would be very slow unless you remotely rebuild your laptop from the dedicated server. I have a small server (1GB RAM, so it's even worse), and I can't rebuild on that server without thrashing.
But if it is just going to be used as a second display, I can see it working. Maybe build an ISO image from config, and installing that would work well.