Yes, it certainly does.
During a power on or a reboot, when the BIOS ("Intel NUC") splash screen appears, press F2 to request entry into BIOS Setup (the Visual BIOS program). Click on Advanced and then Power. In the Secondary Power Settings window, set parameter After Power Failure to Power On. This setting says that, when power is restored, the NUC should automatically boot up. When you exit from Visual BIOS (either by pressing F10 or clicking on the circled "X" in the upper right-hand corner of the screen), remember to save the BIOS configuration so that this parameter change persists.
Hope this helps,