UPDATE: After flashing coreboot with the option to "Enable ECC if supported", ECC RAM still does not work. The screen and lights come on and the speakers emit a continuous high tone. The memory tested was an 8GB stick of 2Rx8 EP3L-12800E from SK Hynix. It is unbuffered ECC to the best of my knowledge. I'll write up my thoughts on corebooting this particular board when I have used it for some more time.
After learning that the 3612QE itself supports ECC RAM in contrast to the stock CPU options and that the QM77 chipset also does, I purchased a DDR3 SODIMM with unbuffered ECC. I have not been aware of any other attempts to test this combination.
The machine did not POST and did not produce any beep codes. Absolutely no response to any input aside from shutting down when briefly holding the power button. Everything returned to normal upon putting the original RAM back.
I suspect the BIOS lacks support, but whether this changes with coreboot remains unknown to me, at least until I learn how to prepare and flash coreboot.
This is purely an exercise in curiosity.
It's usually confined to mobile workstation-class ones, which have Xeon processors. The 3612QE was intended for embedded machines and is one of the few i7 variants to support ECC.