Can I clone a branch of an unrelated remote repo into a branch of my git repo, and keep it updated?

I have a local repo with some code in it in different branches. There happens to exist a git repo out in the world that has the same software, but a disconnected git history. (I don't think it matters, but I know for sure that that repo uses a different branch naming scheme than mine, so there are no conflicts.) I want to clone a specific branch of that remote repo into a new, matching branch of my local repo, and subsequently be able to update it with git pull. Is this possible, and if so... how?