Is it possible to install Desktop edition in Server edition, then access remotely? I can think of lots of applications for this, but don't know if it's possible, or what the drawbacks could be.
you should install ubuntu-desktop and openssl-server
apt-get install ubuntu-desktop openssh-server
ssh -X to access your server remotely.
or you can follow this to config your ssl
As Petrie Wong noted you can install ubuntu-desktop on the server. (This package is the desktop portion of the desktop edition.) If you shutdown the desktop, you also shutdown the server.
You could also run the desktop edition in a virtual machine using KVM. This would give some security separation between the server and desktop. Shutting down the desktop would only kill the virtual machine and not the server.
Normal access of servers is over SSH using the openssh-server package. Programs requiring a graphical interface can be accesses using display forwarding over ssh, and only require a minimal set of x-window programs.
On a server providing a remote desktop, it is common to use a light-weight window manager. A workable desktop with VNC access can be created by installing the packages: xinetd, tightvncserver, xdm, and xfce4-server. Windows remote desktop access can be provided by adding the xrdp package. I documented my setup for Remote Desktops with VNC and RDP.