That it would.

Long ago I read a piece on Cheyenne Mountain. Seems that the mountain was pretty much obsolete before it was completed. The USSR detonated a 100 MT device and had the lift capacity and accuracy to get several to the mountain. The mountain itself would survive, in a somewhat attenuated form, but the initial burst of radiation from any of those warheads would kill everyone inside.

Assuming anyone survived the radiation they would be buried under a hundred feet of mixed semi-vitrified radioactive slag that is pushing 1000F. Where anyone inside gets their air and has sufficient air conditioning to keep from being cooked remains to be seen.

Assuming they live long enough to dig their way out any survivors find themselves in the middle of a radioactive zone twenty miles across. And probably a nation on the other side just slightly more attractive.

Standard orders were that after the initial attack they would hike out and report to their chain of command for reassignment. Right.

As more than one person observed a lot of nuclear handmaidens had an implicit wish to play the high note in a fatal one act play. On the up side they would be going out with a bang. And be one of the first to know about any major event.

But against a tornado. Outstanding.

As one concrete man said - " I guarantee three things about the slab I pour: It will crack, it won't blow away and nobody will steal it".

Concrete is an excellent material for tornado resistance. Combined with the power of dirt you could make it the basis of a home that could resist any tornado. Or the near miss of a moderate sized nuclear weapon.