Νο, or at least not so far. While it may be possible, the atmospheric differences could be as lethal to them as theirs is to us. That, and no Avatar has been shown inside a human structure not breached to the Pandoran atmosphere, at least not yet.
EDIT: When you see Jake and Norm waking up as avatars, they're in a room that's filled with Pandoran air. The doctors are wearing exo-packs, so they don't suffocate from the air. So the avatars can't breathe our air, or the room would be filled with the air mixture that's on Earth, and the doctors wouldn't be needing masks. This is why I believe Na'vi cannot breathe the atmosphere of Earth; because avatars and Na'vi are very close in how their bodies work.
EDIT: The Na'vi and avatars have not been shown breathing non-Pandoran atmosphere so far. While it may be possible or it may not be, James Cameron will have to be the one to answer it. I postulate that the reason that no Na'vi or Avatar has inhaled earth-composition atmosphere is because the RDA didn't understand enough about the Na'vi to determine whether or not they could breathe non-Pandoran air, and they didn't want to risk it. The Na'vi most likely never got close enough to humans to come into contact with their atmosphere. It may be possible but unknown because neither species has had opportunity or motive for finding out.