A few things when discussing nuclear devices...
The Hiroshima and Nagaski devices were both comparatively small atomic devices with a yield in the range of 16 - 20 kilotons. That is roughly comparable to an atomic device which can be fired via tube artillery, or deliveryed via SRBM system.
Another key difference is that both devices were airbursts, with detonation occuring at ~10,000ft if I remember correctly. That means that a person or building at 'Ground Zero' is still going to be nearly two miles away from the blast.
Regarding structures, while some of the buildings did indeed remain standing, they were all damaged and suffered some degree of structural compromise.
Lastly, when the devices went off, the temperature was briefly the same as on th surface of the sun which is why people were scorched into 'shadows' on the ground. Unless the supernatural creature or being is able to shrug off 20,000 tons of explosive force, 10,000 degree temperatures, and the radiation which goes along with an atomic blast, then I would say "no" it/they wouldn't survive.
Now if the device is scaled up to a hydrogen/thermonuclear device, it changes even further. A 2 megaton device, which is one of the standard sizes used for single warhead ICBMs is the rough equivalent of 2 million tons of explosives and the temperature at the blast is going to be somewhere in the neighborhood of 2 million degrees. By way of comparison, the 1980 eruption of Mount St. Helens was also of roughly 2 megatons force. During the eruption, trees as far as 19 miles away that were not shielded from the blast by local terrain were shorn off at the base of the trunk and knocked over. Over 200 square miles of trees were knocked down as a result of the blast. Also, due to the collapse of the crater, Mount St. Helens dropped close to a thousand feet in height.
Treating such a device as something ~7 times as damaging as a shotgun blast but covering a large area is a bit insufficient, especially if someone/something is close to the blast area. The pressure wave is capable of propelling debris like projectiles, with a shotgun-like effect miles away from the location of the blast. In the example I used of the Mount St. Helens eruption, the channeled blast extended out past 19 miles, but with 'only' sufficient force to kill trees by debrading with debris and scorching them, instead of outright knocking them over. Therefore, if looking for a 20 stress type of hit, that might be applicable for someone/something which is about 20 miles from a 2 megaton device going off. Keep in mind also that a 20 stress hit isn't going to result in an automatic Taken Out result for anything with even Mediocre (+0) Endurance as long as they can take Consequences.
In short, there is a tremendous amount of energy in such devices, making a nuclear weapon very much a 'plot device' and should be treated as such.