Continuous Integration (CI) is a software development practice that leads developers to integrate their work more frequently. Software projects have broadly adopted CI to ship new releases more frequently and to improve code integration. The adoption of CI is motivated by the allure of delivering new functionalities more quickly. However, there is little empirical evidence to support such a claim. Through the analysis of 162,653 pull requests (PRs) of 87 GitHub projects that are implemented in 5 different programming languages, we empirically investigate the impact of adopting CI on the time to deliver merged PRs. Surprisingly, only 51.3% of the projects deliver merged PRs more quickly after adopting CI. We also observe that the large increase of PR submissions after CI is a key reason as to why projects deliver PRs more slowly after adopting CI. To investigate the factors that are related to the time-to-delivery of merged PRs, we train regression models that obtain sound median R-squares of 0.64-0.67. Finally, a deeper analysis of our models indicates that, before the adoption of CI, the integration-load of the development team, i.e., the number of submitted PRs competing for being merged, is the most impactful metric on the time to deliver merged PRs before CI. Our models also reveal that PRs that are merged more recently in a release cycle experience a slower delivery time.