I would doubt it. The high concentration of carbon dioxide on Pandora makes it poisonous to humans so I think that Earth's air would also poison the Na'vi.
It's possible that Na'vi could breathe the air of humans, but it is highly unlikely. Their air has a high level of carbon dioxide. The air that the humans breathe is mostly nitrogen and oxygen with very little carbon dioxide. The Na'vi would not be used to the air and would probably suffocate.
EDIT: Seeing as the Avatars were first activated (for Jake and Norm, at least) in an area with atmosphere that required the human scientists to wear Exosuits, this is likely.