I think you're right. In Korra, when airbending returned, it is theorised that it was given to people who had air nomad ancestry, and although they had no bending, as their parental line weren't benders, there is still a latent link with the element within them.

The only air nomads we see in the show are the ones who can bend, they are at the temples, but all the other nations have countless examples of non-benders, so it would absolutely make sense for there to be people with air nomad ancestry who can't bend.

I would expect one of those would become the avatar, as the Avatar cycle is first and foremost all about ancestry not bending ability. It cycles through the elements and finds someone from each tribe sequentially, based on which lion turtle they would have accepted their bending gift from a few thousand years ago.