I have many times just installed Ubuntu on other machines and then just moved the hard drive onto the headless machine.
Just make sure not to install any proprietary drivers (video card, wireless mainly) and make sure to install open ssh-server.
sudo aptitude update
sudo aptitude install openssh-server
I have had to do this on a non headless dell server because it required a special dell disc (it was the only disk it would boot from) that would then let you choose between installing Windows Server 2003 and Redhat something or other.
So I put the drive in a desktop and installed Ubuntu Server on it and then popped it back in the other machine and it booted up just fine.