I see you Tree of Souls People,
It has been suggested that the Na'vi can somehow breath Earth's atmosphere and survive. At first this appears to be unlikely due to normal naturally selected and inherited physiological constraints. In the natural world, all living organisms have adapted to survive the atmospheric conditions that exist on the planet, be it Earth or Pandora. In the natural world there are however always exceptions to the rule in the evolutionary stakes that allows species to survive in different environments.
Both Earth and Pandora have a Nitrogen and Oxygen predominant atmosphere, which is necessary for all aerobic dependant biology like the Na'vi. However on Pandora the concentration of Carbon Dioxide is around 18 %, where as on Earth it is <<1%. Humans will die once the Carbon Dioxide concentration exceeds 10%, and have increasing impaired function as the concentration increases from <<1% to 10%. In addition to this, the air pressure on Pandora is 10% less than that on Earth
For humans, moving from one type of atmospheric condition to another type atmospheric condition on Earth can have serious life threatening consequences if done too quickly or if there are underlying cardiovascular problems. For example, people suffer from altitude sickness, or reverse altitude sickness if they change altitude too quickly. Alternatively they can suffer from the bends if they rise to the surface too quickly when scuba diving at depth. Being of similar physiological appearance to humans, all these conditions would most likely apply to the Na'vi as well.
The Na'vi however appear to have evolved so that they can accommodate the high carbon dioxide atmospheric conditions of Pandora. They however appear to be in a constant state of Hypoxia, where there is little oxygen being carried in the blood stream. A typical symptom of Hypoxia in humans is blue coloured skin. Perhaps the Na'vi have evolved from a low oxygen, anoxic environment. However there is another explanation as why the Navi may have blue skin/blood.
There is one creature on Earth that has blue blood and that is the Octopus. The blue coloured copper based chemistry of the Octopi's blood allows it to carry more oxygen through the cardiovascular system than the normal iron based chemistry of red blood. As a consequence of this, the blue blood allows the Octopi to live in extremes of temperature, oxygen and carbon dioxide concentrations.
I have already hypothesized that the Na'vi have an unrealized ability to change their skin colour like an Octopus for camouflage purposes. When you look closely at their skin they have a spotted coloured skin like an octopus. Like an octopus, these could be neurons, just like that found in the brain.
If the Na'vi do have Octopus type blood and cardiovascular type system (NB: Octopus have 3 hearts), then it may be possible for the Na'vi to live in Earth's atmosphere, however they would probably need to undergo a gradual acclimatization period to do this.
That's my thoughts for now,
Eywa ngahu