Can I unplug my Mac mini from power once it's in hibernate mode?
You shouldn't unplug your Mac unless it's shut off; however you can do it using hibernate mode. The closest to hibernate is in this answer, How can I manually put a Macbook Pro to hibernate without going to sleep mode first?, it outlines how to enable hibernate on your Mac, which it actually copies the memory to the disk, and if you loose power, it restores the memory. It's made for MacBooks, but will work fine for any Mac.

The Reopen Windows feature should work, but I don't like using at, as it can significantly slow down startup (and login) speed.