Good theory, however, next time, try the Question/Answer thread at the top of the forum.
Anyway, no one would be able to learn Airbending from Appa, here's why. Back in times before anyone bent the 4 elements, people were not born into nations, because there were no nations. The nations were named after the 4 bendable elements, which had not been bendable at this point. A group of nomads began learning Airbending from the Bison, as other nations began learning their bending from the Moon, Badgermoles, and Dragons. After "bending" came into play, the four nations were created, each named after the element that the people there bended.
Since bending was a major factor now, a new "law" of nature eventually came up: You can only bend the element of the nation you are born into. The reason being so that no one would be more powerful than the Avatar: the only person who can bend 4 elements.
Now onto Appa. The basic reason someone couldn't learn Airbending from Appa, is because they would have to be born into the Air Nomads to do so. Since Aang is the last Airbender, the only way to birth a child into the Air Nomads, is for Aang to have children with someone, like Katara. However, we do not know if these children would be considered Air Nomad or Water Tribe. (They couldn't be both as it has been stated that each person can only bend 1 element except for the Avatar)
By some off chance this child is born into Air Nomads, he would not need to learn from Appa, as his father, Aang would teach him.
In conclusion, the only way to bring Airbending back is for Aang to have children, as no one would be able to learn from Appa due to the fact that no one besides Aang is born into the Air Nomads.
Hope this clears things up.