As is explained (in imperfect, but essentially correct) manner in the blog itself, I believe "Duski" said it best in his answer:
"it is posible that an helicopter gets sucked into a hole, if it is big enough (read deep enough). That is because earth is hotter underground, and if you get deep enough, you get a “Termal Borehole”, when the difference in temperature causes a stream of hot air.
"Now, when a helicopter enters such hot air stream, he no longer can sustain his altitude because he is adjusted to the colder air outside of stream, that is thicker then the hot air. The hellicopter is going to fall so long until the pilot adjusts the speed of the rotor to the hot air (if the hole is very deep, the air is too hot [then] the helicopter is going to fall before the helicopter [pilot] achives enough power).
There is also a stream of colder air, that streams into such a hole, and again, if a hole is deep enough, that is a powerfull stream that easily slams a helicopter into [the wall of the hole] ground or into the wall of the borehole."
(Spelling corrected by me.)
In essence, it can and it can't, depending on the altitude, the skill, and the quickness of the reflexes by the pilot of the helicopter.
As for a no-fly zone, I doubt it. There might be a NOTAM (Notice to Airmen) existing about the area to warn pilots that there is an aberrance in the flight patterns, but only in very rare instances (e.g., over the White House or Capitol Building, or in militarily imposed areas), are true "no-fly" zones imposed.
