Can I unplug my Mac mini from power once it's in hibernate mode? Suppose I want to work on my Mac mini here, reach a certain point in my work, then put it in hibernate mode and unplug the power.

From what I understand the hibernate mode will save the status of the Mac into the disk, and will unpower all devices. So, from what I understand, I can now unplug the Mac mini and no damage will occur. 

In principle I can take my Mac mini into my messenger bag, drive 2 hours to home, and once at home attach it to a power plug with its cord and power it back on. At that stage the Mac will take some time to restore from disk, but I will have got the same status of my Mac as when I switched it off.

Please note this is not the same as "reopen current windows", because certain programs have a more complex status than just having an open window and its position. For one example (and there are several) you can think to Terminal.app. If you have multiple tabs open each history of commands is preserved separately until you quit the Terminal.app, once you quit only one tab history is saved to file and persist to your next reboot (btw, I am aware there "fixes" to this behaviour, but they do not apply to my actual case, I just need to carry an example). 

Do you see any flaws in my story? Is it really possible to unplug the Mac mini once it has gone into 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.