As we have already said, since there is no licence attached to this code, the starting position is that you have no rights to copy or use it. However, as we have also noted, GitHub's terms of service require anyone publishing publicly on the site to permit other GitHub users to locally-fork the code, using the site's fork button.
So you definitely have a right to create a GitHub-hosted fork of the code, in order that you can add the licence and submit a pull request (which as Philip Kendall notes above, anyone may do for any reason!). But you may not distribute this code to anyone else, so a public repository would be a mistake (and, indeed, a violation of the original rightsholder's copyright). I don't know if the GitHub site mechanics let you submit a PR from a private repo, but if they don't, GitHub-forking is not the way to go.
It may be that the rightsholder has already expressed a clear desire to release this code under MIT. Licensing doesn't require anything more than a clearly-expressed grant on the part of the rightsholder, so if (s)he has been clear about releasing the existing code under MIT, and has so far simply failed to add the actual licence text, then you could reasonably take and use it under those terms now. That is ground whose solidity you will want to be sure of before you stand on it, though, and you don't link to the project or to that discussion, so we can't comment on the specifics of this particular case.