There would be like, Ember Island Players plays made with scenes like THIS: http://3info2u.com/Image/Princes_in_the_Tower_Painting.jpg , where Iroh would steal upon the two helpless children in the night and it would be full of drama and woe.

I can definitely see some unscrupulous non-Fire Nation types trying to get to the heirs FIRST for ransoming purposes. Also, Zhao would be looking, for the glory, if he has to put invasion plans on hold ANYWAY...