Man I just checked it out on Google Maps (search Hard Luck Castle)... it is truly in the middle of nowhere, around 25 miles north of Death Valley National Park. That means trucking in a lot of...everything. Gardening/livestock is gonna be hard in the summer when it's over 100 degrees every day. Resupply? Forget it in TEOTWAWNI situation, as there's no one around to trade or barter with. No towns or anything around.
As to defense...first, no one is likely to stumble upon the place. So defensive needs are low. But, it's not a very defensible location. High ground to the west and north would give good fire angles on the building. Can't tell from any photos I've seen if there are windows facing north and west, or if you would have to or be able to defend from the rooftop against sniper fire from the north and/or west. Now, against a group of determined attackers, it looks like there are a lot of blind spots on the perimeter of the building. You would need a good number of people to effectively defend it.
It's kind of a neat building. Put it in a forest, or near a lake (maybe with a spring underneath for water), and with that mine, and redesign the window lay out, and it might just be a good modern castle.