Well, that would technically buck a piece of series canon (that ALL members of the Air Nation could bend; so there'd be no "nonbending" children to leave) But I suppose it is a possibility.
What I think is more likely is a variant wherein the increased spirit background has cased the development of additional benders from ALL tribes, according to their decent. That is, some non benders of Earth heritage can now earthbend, water can waterbend, etc. Bumi is part air, so air is as likely as water. The other new airbenders could be the result of other persons with air blood from the days of pre fire nation peace (basically the same scenario you stated, except that in this one, there are no "nonbenders" leaving the Air temples, just their DNA spreading around.) The fact that they seem to all be in the new air nation could simply be an aptitude thing, maybe you also has an influence on you preferences (i.e. maybe all of those who came to form the new air nation actually had air blood in them from way back, and it is this blood that caused their liking for the air culture.)
"For I have heard the Song of War, and to me, it sounds just like "Please, Mister Custer.""
Cogito Ergot Sum, "I think there is something wrong with this rye bread." (Aplogies to Seafrol.)