Mmm... Personally I don't think it would have greatly changed the story. Perhaps it would have merely delayed things.
I'll explain myself:
Sakura had been reevaluating her perceptions about Naruto and Sasuke for a long time. The bench scene started that change and the Forest of Death sped it up (during that ordeal she realized Sasuke wasn't so wonderful and perfect -she called him a coward to his face- and had a dark side she had never taken notice from... and frightened her). After the Forest of the Death she never again squeals: "Sasuke-kun, you are so wonderful!". And during the goodbye scene she tells he never talks to her and she thinks he hates her. And after he left anyway, she was very shaken.
And then we got The Promise of a Lifetime scene, where her last preconceptions about Naruto also shattered forever.
Keep in mind the change we are talking about is posterior to those scenes.
Later, when she and Ino went in the hospital, she told she was visiting Naruto first (matter-of-factly assuming he had fulfilled his promise).
Thus, I don't think Sakura would woo Sasuke how she used to (certainly she would not behave like a fangirl. She had ditched that act long ago). And she would never see Naruto and Sasuke with the same eyes. Maybe she would be more protective of Sasuke since she would be frightened of him leaving again, but I doubt she kept hopes or dellusions of being his girlfriend. And she would feel closer to Naruto.
Maybe she would ask Tsunade becoming her disciple not matter what. Rememberer: she told she would go with Naruto the next time... but she hated being a burden and being left behind. So she could have wanted being trained by Tsunade (who she had been alreay impressed over) even if there was no Sasuke to rescue. Moreover, she could think if she proved Sasuke his teammates weren't a burden, he could stay... or she could help if he left again.
Naruto wouldn't be depressed about Sasuke but he might become more protective -and watchful- of him. Jiraiya would offer him training anywaydue to the Akatsuki threat -and they would have not deadline for completing it-, but perhaps Naruto would want staying in Konoha in order to watch Sasuke.
Sasuke would try leaving again. He had left his hometown willingly because he was jealousy of Naruto and he thought he was becoming weak cause his friends. Getting dragged back would not change that. In fact, he could become more resentful of his friends and his village. And it is likely he would get punished by his defection and the other Rookie Nine would be resentful of him, so it would increase his fury, frustration and resentment.
And if Naruto and Sakura were trained by Jiraiya and Tsunade how I have reckoned, he would be EVEN MORE resentful. He would wonder why those weaklings could be trained by legendary shinobi but he was denied such training, he would get jealousy of them because they were becoming stronger (which in his mind means he is becoming weaker), and he would think he was right: that village and those partners were weakening him.
So he would want leaving again. I am sure of it.
I am not completely sure how it would have changed the story afterwards, though.
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As for my signature...I just want to humor a little all this 'pairing war' because, you have to admit that it kinda hilarious and it have been a long time since we didn't hear all that madness (the chapter 437, it was NarHina, now, it will be SasuSaku)
But seriously, I don't fear for NaruSaku....why should I?
I agree. It would amusing if it was bot so tiresome. Everyone seem so sure usually, but then some drama ahppens, and everyone panic.
But yes, it is chapter 437 again... Or chapter 408 again... Or chapter 355 again... Or chapter 306 again... Or chapter 283 again... Or...
Developments NEVER happen in this manga how NH or SS fans expect, hope or want. I have learnt that lesson after several instances where I admitedly worried... and then I found out I had got worried about nothing.