GitHub data can provide valuable insights into an engineering team's productivity and performance. By using a connector like Fivetran, companies can gather information about issues, pull requests, and commits. Metrics such as the number of opened issues for bugs, code hygiene, and new features, work dedication to each category, and time taken to close pull requests can be analyzed. This data can help identify areas where improvements are needed and track the effectiveness of different strategies. Additionally, integrating GitHub data with other sources like Zendesk or customer support data can provide a more comprehensive understanding of product health.