I definitely think it would help, or like you said, wouldn't hurt. At worst, the fans of Spike like me would be happy with his story, and the people that don't like him would not have a reason to hate him even more. Its not even that I want the character to do a 180, it's okay to show that he's in love and Buffy, but dam he can still do his own thing. They don't have to remind us every two seconds that Angel loves Buffy, so I don't know why they are doing that with Spike. Especially that Spike showed a lot of potential in early seasons, he has an interesting past, why not explore that. They could give him a story with Dru, make something interesting there (since a lot of fans also like that pairing). Just anything but the roomate story, that just sounds awful.
I think if the writers had continued to point out in every episode that Buffy and Angel still love each other it would have destroyed the ship and the characters. Neither of them could have grown or had other experiences if they had done that, which is exactly what is happening with Spike. The fact that Buffy and Angel led new lives made what they had more interesting. It gave them more dimensions and their experiences more texture. They continued to be individuals with agency and that is why Angel could sustain 5 seasons of his own story, and continues to sustain, if not surpass, the original story (BTVS.)
I don't know if unshackling his narrative would cause people to stop hating Spike, but it might just present them with an opportunity to like him.