The Scarlet Letter

Does the birth of "a lovely child" born out of an adulterous relationship prove that the strict Puritan moral code is wrong?

The birth of the "lovely child" would be seen as a product of God's grace. As she grows, Pearl will become more and more of an enigma as she develops some strange personality traits. Her mother will consider her an "elf-child" and when questioned about her origins, she will say she was plucked from the rose bush near the prison door. She will often ask about the minister, as if she has a strange and connection to him. Even though Hester has to fight in order to keep custody of Pearl, the girl will both a joy and a penance for Hester.

I don't think it proves that the moral code is wrong.  What I do think it suggests is that, despite the moral judgement that the community makes on Hester/Arthur, nature accepts Pearl as another of her children.  This is visible in Chapter 19 where the brook an agent of nature, reflects/accepts her beauty without reservation.  Water, in addition to its role in nature, is an agent of cleansing, and an important part of the Christian rite of Baptism.  The "wild flowers" in her hair are also a sign of her acceptance by nature, and continues the symbolism of the rose bush that greeted her when she and Hester exited the prison. 

The fact that Pearl is beautiful is proof enough of God's love.  Had Pearl been meant to be solely a punishment to Hester as well as justification of the system of law in Puritan society, Pearl would have been made deformed or ugly beyond belief.  Hawthorn doesn't do that to Pearl, even though he himself was suffering as a result of his own ancestors' involvement in the witch trials of Salem.  All children are blessings...none is a mistake as they are all part of God's plan. 

Pearl's birth, accepted by Nature, is, perhaps, an indication that the Puritanical moral code is too strict as it condemns forever the sinner and the product of his/her sin. 

This lack of forgiveness for one's sin is a reason that Dimmesdale is afraid to confess.  Hawthorne views this strict, unforgiving property of Puritanism as the cause, then, for hypocrisy and the harboring of "secret sin."  His theme, "Be true" reinforces this belief.