No, Nick giving into Amy's demands at the end of Gone Girl doesn't prove that his retelling of the events was less than truthful.
We know that Amy is an unreliable narrator through her diary. However, that was deliberately written to frame Nick for her murder. When she's speaking outside the diary or when we're being shown events from Nick's perspective, it's likely that both are more reliable narrators. Statements he makes to people in the novel are true, and he doesn't reveal everything to the reader right away. However, as a narrator, he doesn't lie directly to the reader.
Ultimately, Nick may hate Amy. However, he still chooses to be with her. It doesn't mean that what occurred didn't happen or that it didn't affect him. It means that Amy chose the right approach to keep them together after they reconciled. She used his sperm sample to get pregnant with his child. Nick wanted a child and wouldn't leave it alone with Amy after everything she did. That's why he decides to give into her—not necessarily because he's dishonest to the reader.