So, I gave it a go. Fanless seasonic 400 W psu with gtx 1080. No overclock of the cpu or gpu.
System boots, usable in windows.
I launch total war attila, go into graphics options and put everything to max quality. The benchmark "Londinium" runs ok. When I want to start a quick battle, the screen goes black with a loud "beep". The system restarts with a message "power surge detected".
I try Civ Beyond Earth with all options to Max. For some reason the game is capped at 50 FPS. It works fine.
Last, I try the Witcher Enhanced Edition with all settings to max. System crashes after the intro with the same "power surge detected" message.
To sum it up, it works as long as you don't do taxing stuff. Obviously under heavy load the 1080 uses more than 180 W. Could be GPU boost doing an automatic overclock when temps allow it. Now I have to wait a few more days to get a more powerful PSU, and even more annoying I will have to redo all the cabling.
TLDR : does not work...