In The Scarlet Letter, what is the purpose of the wild rose, and what does it symbolize?

The first chapter of The Scarlet Letter opens with a description of the prison door, specifically the prison where Hester Prynne has been held since it was discovered that she committed adultery. But at the end of this short chapter comes this sentence:

But, on one side of the portal, and rooted almost at the threshold, was a wild rose-bush, covered, in this month of June, with its delicate gems, which might be imagined to offer their fragrance and fragile beauty to the prisoner as he went in, and to the condemned criminal as he came forth to his doom, in token that the deep heart of Nature could pity and be kind to him.

If the reader has not read "The Custom House," the pseudo-introduction to the book, then s/he will have no idea what the rose symbolizes. However, the next chapter jumps directly into a description of Hester and her sin, thus linking the rose to Hester. As she exits the prison for the first time, her baby held to her bosom, she is described as beautiful and as a lady, bearing the scarlet A emblazoned on her breast. The color of the scarlet letter matches the red of the rose, a symbol of love and passion that does not belong to the Puritan society. As well, she is a symbol of purity and light at the end of the book, foreshadowing the end of the novel here in the first chapter.