Ubuntu Desktop as server...
This is fully possible, but on Ubuntu Forums I saw a similar thread/question to yours. The general consensus there were to install the Server Edition, and then add the graphics later.
Reason for this, is as ashwin_cse says: Server packages are meant for more stability and uptime. But it can be OK, when you log in to make changes to the server, to see a GUI. Also, if you install the Server Edition, you won't get all the desktop programs like office suites, word processors, games (the few that come with Desktop), utilities you would need for a desktop, but not a server.
My suggestion/advice would be to ask how you can install a GUI to the Server Edition, not how to make Desktop act like Server. (Or better yet, search the forums here and on UbuntuForums for the answer. It has been asked and answered, believe me.)