Agree with Shayki Abramczyk, the answer is No. But I think maybe you need more descriptions to help you understand ~
In your situation, you set build pipeline as release pipeline's artifact. If you've checked this document you would find these statements:
1.When authoring a release pipeline, you link the appropriate artifact sources to your release pipeline. For example, you might link an Azure Pipelines build pipeline or a Jenkins project to your release pipeline.
2.Note from here: You must include a Publish Artifacts task in your build pipeline. For XAML build pipelines, an artifact with the name drop is published implicitly.
3.Auto-trigger releases feature(CD trigger in artifact): New releases can be created automatically when new builds (including XAML builds) are produced. See Continuous Deployment for details. You do not need to configure anything within the build pipeline. See the notes above for differences between version of TFS.
To sum up, the artifact source here represents a build pipeline instead of the outputs of a build pipeline. So when you enabled the CD trigger in artifact(in your situation a build pipeline), the release is triggered whenever a new build finishes. And this behavior won't be affected by whether the build pipeline has Publish Artifact task to publish the outputs from it.
For the 2.Note: It can be considered as we must include a Publish Artifacts task in build pipeline so that the release pipeline can access the outputs of build pipeline. And then we can deploy the outputs(.dll/.exe or what) to target machines/environments. (Actually we think the must in document should be replaced with It's recommended to/should)
Publish Artifacts task make the build+release process meaningful. Cause if our release pipeline can't access outputs of build pipeline, what should we use to deploy? But whether this task exists or not won't actually affect the CD trigger. (Just like the third statement:You do not need to configure anything within the build pipeline)
