During the evening's festivities in Silas Marner, how much progress does Godfrey make in winning Nancy's approval?

The festivities in chapter XI bring Nancy and Godfrey closer than ever with a unique chance to sit and talk alone.

This chance came as a result of a wardrobe malfunction that prevented Nancy from enjoying the dance fully, and it gave Godfrey a chance to move her somewhere else. He was very happy at the chance, and made some bold moves throughout their conversation.

[Godfrey] got rather bold on the strength of her confusion, and was capable of leading her straight away, without leave asked, into the adjoining small parlour, where the card-tables were set.

Nancy, on her part, was equally excited. Her personality is so complex—and her behavior so strange—that it is hard to extrapolate her exact feelings. After all, Nancy is described as someone so obsessed with appearing and acting righteous and proper that she sometimes loses herself in the process. Nevertheless, she does show some glimpses of her interest in Godfrey that he definitely picks up on.

Therefore, while their entire conversation is awkward, and Nancy does not want to let go of her self-control, Godfrey makes clear gains in the journey toward Nancy's heart. He has not entirely won her "approval" as far as being a formal love interest, but it is clear their feelings are mutual despite the obstacles blocking their potential coming-together.