How might Hester's life have turned out differently if Pearl had not been born?
In Chapter 13, this might be explained, but I have a hard time understanding Nathaniel Hawthorne's verbose writing. Thank you!
I'm not as hopeful about Hester's future if she had not had Pearl. The Scarlet Letter is about just that--the guilt, shame, and consequences of sin, and in this case the sin of adultery, as represented by a scarlet letter. It's true that Hester has made peace with her sin and her position in this Puritan world because she had to; however, unlike Arthur, I think Hester would have acted in exactly the same way if she had the chance to do it all again. She is not particularly bothered by the vilification of the women; she clearly doesn't like their treatment of her, but she also clearly doesn't regret her behavior. Pearl is actually the reason the affair ended, we must presume; without her, Hester would have been content to continue the illicit relationship with Arthur. He, on the other hand, would have eventually put a stop to it out of guilt, based on the connection we see between his guilty conscience and his weakened body. Others, as suggested in the post above, have forgiven (or at least overlooked) Hester's sin; Hester, because she has Pearl and the hope of a future with Arthur, is not particularly concerned with their forgiveness one way or the other. (She says later that if she were worthy of it, the letter would fall off on its own.) Pearl is the human embodiment of that letter; without it or Pearl, Hester would have been even more devastated when Arthur was one day unwilling to continue their affair.
Assuming everything else, including her relationship with the baby's father, were the same, the one exception being the birth of Pearl, it is likely that Hester's life would have turned out much differently.
Chapter 13 focuses on the changes that have taken place in Hester in the first 7 years of wearing her punishment. These chapters tell of Hester's goodness and the way she uses her talent with the needle to provide for the poor. In the eyes of many, the "A" on her breast comes to stand for "Able" rather than "Adultery." As a result of wearing this Scarlet Letter, however, Hester has grown old and wise beyond her years. While the letter has robbed her of her beauty, it has given her a sense of compassion and understanding she might never have otherwise discovered.
Ironically, Hester does not view her new self with a sense of pride nor contentment. She longs to feel equal to the other women. Knowing this is never possible, she continues in silent misery, accepting the punishment for her actions, but refusing to be forced into a sense of guilt.
I think if Hester had never had the baby, and the public never knew of her sin, any number of things would be different. Because she was so beautiful and so talented in creating things of beauty, it is possible the women in the colony would have hated her anyway. It is also possible that the secrecy of her sin would have begun to wear at her inwardly in the way it wears on Dimmesdale.
There are almost an infinite number of speculations one could make about how Hester's life might have been, but I think the purpose of Chapter 13 is to show some of the positive things that resulted from Hester's mistake. Perhaps in other circumstances, she never would have gained the sense of selflessness and charity she develops. Certainly she would not have received the almost 6th sense she has of empathy and wisdom.