nope a single server can boot hundreds of different clients, yon can share parts of the clients and separate other parts. you can even have files generated on the fly as the system boots. The server does not have to be on the same network or even be the same architecture. At present my laptop has about 5 different thin client images on it which i am refining.
probably the biggest issue you will have is changing the startup procedure of the linux distribution you have, but once you have done this you will have one very easy network to manage.