first I want to post that we already know Avatars can have kids (avatar Roku had at least one of the parents of Ursa, the mother of Zuko)
second: it should be HIGHLY unlikely that the avatar would have a child or grandchild that would be the next avatar, but technically is possible, for example
Aang and Katara have a child, and that child marries and has a child, and the child is born the same day or a few days after Aang dies, and it is a waterbender, that child could be the next avatar
third: thanks to the "energy bending" Aang displayed at episode 321, we can say that is possible that Aang can do the reverse of what he did to Zuko's dad, and could give the ability to "element bend" to any non-bending person, including ability to airbend (perhaps the people at the north temple? who airglide)
so he doesn't necessarilly have to have tons of kids in order to re-establish Airbending culture