I think even if he killed Aang the new Avatar would just be born but then there would be no one to teach he ou she airbending and it would just throw the world out of balance cause there is bound to a point where the Avatar 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 Avatar 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 Avatar cycle, he would have had to kill the Avatar while in the "Avatar state", so yes, probably just ending an Avatar's life would just déplacer on to the suivant cycle...at least commander Xaio realized this when he captured Aang in "the Blue Spirit" episode.