I can confirm that the DN2820FYKH can boot fine without a monitor.
There have been issues with some BIOS versions; I am using BIOS 47, dated 24.12.2014.
Operating system is now SparkyLinux with Openbox, Version 3.6, with EFI boot. Setting up EFI boot was on-trivial, but possible; I can post some hints if anyone is interested. Note however, that I had to tick the "Legacy Boot" box as well as the UEFI Boot box to get the NUC to boot without the monitor. However, I have verified that it is indeed booting in EFI mode.
I had previously checked that headless boot was possible with Ubuntu Server 14.04, with the same BIOS. It was not possible when I had BIOS 40.