naruto would be absolutely devastated, worse than jiraiya's death. he would certainly not be running to hinartas hanarms because hinata never was shown to care or know sakura much and so cant offer any words of true comfort. only ino would be able to or maybe tenzo since tenzo noticed how much sakura cared.
as for story, sakura would never have gotten to the sand so kankuro and by extention chiyo and gaara all stay dead. she doesnt go to the bridge meaning she isn't there to heal naruto's rampage vs orochimaru and subsequent chakra burns. naruto is miles away from any other help and dies a slow painful death. sakura is not there to save karin's life in iron country. kurama is revived and captured by obito via sharinhax then sealed in mazo by akatsuki. obito brings about juubi's revival with the eight tails piece. and since he probably cant become its jin juubi destroys the world.