How to use Git with Drupal 8 when using composer
Short answer: no, you do not need to commit the vendor folder, because the contents are built using composer.lock and composer.json (both should be committed) when running composer install. Some people have to commit vendor due to their hosting constraints and/or having no build process (where the application is built for deployment).

IMO management via Composer with vanilla D8 tarball is very difficult as it lacks the structure to facilitate solid version control, project management and patching workflow that others like Drupal Project or Acquia BLT offer.