I dont think it need a monitor to boot.
However if no monitor is connected/identified during boot the graphic will be disabled (which is a common thing) to save power.
Now the problem comes when you run a GUI based OS such as windows, because according to windows there is now suddently no graphiccard to draw the GUI at so it will fail.
Compared to lets say a Linuxserver who doesnt need any graphiccard to handle incoming SSH-connections.
There are hdmi-plugs one can buy and connect to the output which will fake a monitor so the graphics driver will be happy and the OS will be happy to have a graphic card to draw its GUI onto (and suddently you can now login through RDP to your Windows box).