Right. Let's get to it. Before anything else lets look at how Sasuke and Sakura got together.
He had just lost his arm, reflected on what he had been doing, and admitting defeat. When Sakura appears after some pondering he apologizes to her for how he behaved. Then he leaves for his wandering to find atonement and implies to start a relationship with her.
Sasuke felt sorry for how he treated Sakura, so he got together with her to make up for it. That doesn't mean he ever fell in love with her.
What happened after they got together? Well, he kept on wandering to the point he spent 12 years going out of his way to not see his wife or daughter. After he stopped doing that, while he cares for his daughter, he never mentions his wife Sakura. Seriously, after Kodaichi left she cease to exist in the manga.
Now. Lets look at Sasuke's thought and behavior around Sakura.
The Bench scene he chewed her out for her rude comment.
Before the Chunin exam, he chewed her out for focusing on trying to get a date with him, instead of training as she had fallen behind Naruto as far as he was concern.
Him leaving the village, he makes it clear, he doesn't have feeling for her, while he did enjoy the time he spent on team 7, she is not that important to him, and he only cares about revenge and is willing to abandon everything to get it.
After leaving the village he doesn't comment often on his feelings towards Sakura. However, both times he meets her he tries to kill her and people around note he has no hesitation in his attempts.
693. Kakashi asks why Sasuke mistreats Sakura so much when she loves him. Sasuke makes it clear he doesn't love her, doesn't understand why she loves him, he himself doesn't understand what she see in him to make her like him, and thinks she is just delusional.
So Sasuke doesn't hide the fact that he doesn't like Sakura and he thinks she should stop chasing after him. He doesn't say it all the time when they are teammates because its rude, but he will say his peace if he feels prompted. Once he leaves the village, he just stops caring about Sakura seeing her as nothing more than a deranged annoyance.
So how would if Sasuke didn't leave the village go? Well, they were only on an active team for a short amount of time before Sasuke left. The time between Sasuke leaving and the end of the War arc is about 3-4 years. While that may be three to four years to bond and fall in love...That is also, three to four years for Sasuke to get tired of constantly telling her, "leave me alone, I don't like you, and I don't want to date you." Till he finally snaps and ask her why she even likes him. She tells him about the bench scene. He tells her that it was Naruto.
Also Naruto held himself back for all those years due to his promise of a life time. No promise, means he is free to try and win Sakura's love.
The difference between Naruto and Sakura in this scenario. Is that Naruto will continue course of training and growing stronger. Sakura will likely languish as while she has the desire to grow stronger, she only got the drive after seeing Naruto injured trying to fulfill his promise to her. That doesn't happen, she likely won't go to Tsunade for training and languish in mediocrity. Which will keep making her look worse in Sasuke's eyes. Making it less likely for him to grow fond of her, but more disgusted with her.
So the answer is No. NS was suppose to happened but the pairing changed at the last second. Sasuke always dislike Sakura and didn't want together with her till a mandate order them to get together. Leaving or staying wouldn't have changed anything.