Like most of biology, it's not a simple trigonometry equation. You hear primarily in two ways:

Pressure on the inner ear
Bone conduction, mostly from vibrations of the skull

Air pressure is not reduced by these headphones, neither are the vibrations being picked up by your skull. Your inner ear is still getting a workout. Soem users of these headphones report side effects of nausea and an uncomfortable feeling of ear pressure, all symptoms of hearing damage. As the technology gets better, these side effects are being decreased -- there's hope for the technology yet.

When you combine this with the increased possibility of hearing damage while using headphones, it makes it hard to gauge what is and is not a safe volume level.

Which is not to say that anti-noise technology can't have significant benefits. If it means you aren't blasting music through headphones to hear it above the outside noise, that's a safety benefit. The psychological benefits when used to reduce your perception of crying babies on a plane is probably priceless depending on your tolerance level.

But as protection goes -
A set of high end Bose headphones is $300
A set of high end earplugs is $250
The cheapest noise-canceling headphones are about $50
The cheapest functional earplugs are available for free at many ear clinics

Here's a paper on the ANR techology. In summary, in less than 1% of high noise environments did anti-noise technology prove to be an improvement over conventional hearing protection.