Hello,
I found this discussion looking for a solution to the exact same problem.
My recently bought Intel NUC 3815 do not boot if no screen is connected to it when using late BIOS.
The installed OS is Debian Jessie amd64 with no desktop environment.
The explanation and solution given by Sylvia do not solve the problem as I assume it occurs before the OS (and so the VGA driver) could be loaded.
I had this issue after updating the BIOS to the 0041 version of December 2014.
Furthermore, the NUC boots and works perfectly with no screen (neither keyboard nor mouse) when the original March 2014 BIOS 0014 is used back.
I can then control it with SSH perfectly en even VNC after installing Xorg and x11vnc server.
I did not try other version of the BIOS.
I hope that Intel will find a solution as I purchased this model to make a small server managed remotely.
Regards,
François