This isn't quite ASB but probably borders on it.
King was known for having pacifist and socialist views during his lifetime, which automatically becomes a huge liability in any presidential campaign. J. Edgar Hoover even lau ched a huge investigation of him hoping to bring him down. Plus, while he was alive, more Americans viewed him unfavorably than favorably. One last obstacle you have to overcome with this AHC is the fact that at King's autopsy, doctors revealed that at 39, he had the heart of a 60 year old man due to all the stress of leading the civil rights movement, so he might not have much time to build a political career.
However, you know what they say, stranger things have happened...