the avatars powers are part of him. if he had kids he would still be the avatar becuase thats his bending ability-all of them. if he other benders can have kids and not lose their bending, the avatar wont either.
In this image avatar Roku's wife, Ta Min, is seen escaping from the eruption in episode forty six in a barco with three people who could be their children. Roku never lost his powers so I guess the avatar can have kids.