How would Belle's relationship with Gaston have developed if he had saved her from the Beast?

This is a question that I've considered for a while. So what if Gaston didn't throw Maurice out of the tavern that night but instead, went with him to the Beast's castle and saved Belle? Surely, she would have been grateful but would she also soften towards him and encourage a better relationship between them? After all, when the Beast saved her from the wolves, she was more receptive towards him and look how that panned out.

To be clear, I'm not suggesting that Gaston's attitude would change as the Beast's did. I believe he would still be as arrogant as ever, if not more so. However, I do believe that Belle may have had a slight change of heart towards Gaston if he had saved her on that fateful night.