No, the Library Folder is not required in the repository and it should not be checked in.
You do need to include your Library folder in the code repository, as Unity Cloud Build automatically generates the Library folder when it processes your project for the first time.
Note: Library caching is activated by default to improve the build speed after the first checkout. You can, disable Library caching in the Unity Cloud Build options if it causes problems.
For more information on the build process, see Cloud Build Advanced Features.
For more information on publishing builds, see Publishing Builds.
For more information about Library caching, see this forum post.
For more information about the Library folder, see this forum post.