Yes, I use Tumblr to build backlinks to my sites.
Expired Tumblrs are very easy to come by (keeping them may be another story). There are plenty of tutorials online that explain how to find them.
Basically, you want to find Tumblrs with good metrics & then drop a few backlinks to to your site. You can set up your bot to follow / reblog / like / etc, but it isn't necessarily needed. You just want the link with your keywords.
Let me know if you have any specific questions.