On laptops you need to have a mouse keyboard and a screen connected if you want to be able to keep it turned on in clamshell mode. Can't say about desktops.
An interesting way to achieve this that I've recently discovered is that I can use Apple's built-in Screen Sharing application to act as the keyboard, mouse, and display when connecting to a clamshell MacBook Pro. The MacBook Pro then only needs to be connected to power and the network.
