I think even if he killed Aang the new アバター would just be born but then there would be no one to teach he または she airbending and it would just throw the world out of balance cause there is bound to a point where the アバター would need airbending and even if the cycle continued when it gets back to air the cycle would end cause there are no airbenders left
He thought he could kill Aang and end the アバター Cycle. Without Airbenders, the cycle would end, and so would the return of any other Avatars. It would've been a win/win situation for Sozin, but he failed (Thank goodness xD).
in order to end the アバター cycle, he would have had to kill the アバター while in the "Avatar state", so yes, probably just ending an Avatar's life would just 移動する on to the 次 cycle...at least commander Xaio realized this when he captured Aang in "the Blue Spirit" episode.