In a way, no. avatar wasn't made in Japan, so in countries other than japón it is not considered an anime. But in Japan, "anime" refers to any form of animación regardless of nationality. Therefore, in Japan, it is considered an anime. It is not considered an anime in other countries such as the United States.
It's sort of a confusing choice between cartoon and anime, since anime refers to animación made in japón and avatar was made in America it would make más sense for it to just be a cartoon.
Well, "anime" is the Japanese word for caricaturas and animation, so, in a way, yes, but anime really refers to the Japanese made cartoons, so in another way--no.