Tumblr importer

Not really, no.

The importer is an automated tool that grabs content already published in one place and republishes it in another. If you were importing from WordPress to WordPress, then publication status would be imported as well.

However, the Tumblr importer uses the Tumblr API to grab everything on your account. If the post is published on Tumblr, it will be imported as a published post on WordPress. If it’s saved as a draft, it will be imported as a draft.