Whether she believes it or not isn't something you can't control. Standing your ground and walking is what you can control. If you lead, and act like a man, and refuse to reward bad behaviour she will know you are a guy she can admire.In theory this sounds good but how would a woman know what's going to happen if she breaks up with you before it happened?
Telling her that isn't going to necessarily make her believe it because in her experience guys probably tell her things all the time and then backtrack.
So I doubt this would play any role on whether or not she stays or goes.
When a woman knows your boundaries and knows you are the type that will not let his boundaries get crossed a chick won't want to cross them. She will be sorry to cross them.
Reward a bad behaviour and take her back and put up with her crap and it will be you that will be sorry.
No second chances. You say this would have no bearing on if she stays or goes? Of course it does. Throwing her a$$ to the curb, she is gone.