Michael Jordan's brother who is more athletic than him?
(him = Michael Jordan)
Is the above sentence fragment grammatically correct? Is the pronoun usage correct?
No, because there is no verb here.
Breaking down the sentence, you have the subject: "Michael Jordan's brother". This is followed by the clause describing the subject "who is more athletic than him". That's it.
It has the same structure as the sentence, "My friend, whom I adore."
This aside, "him" could imply Michael Jordan, yes. Though you would probably say "Michael Jordan himself" to be explicit and for clarity.
Maybe you meant to say:
Who is more athletic than Michael Jordan's brother than Michael Jordan himself?
For nearly two hundred years prescriptive grammars taught that the nominative, he, was correct there, and that the accusative, him, was incorrect. You may still find texts where that "rule" is presented. But your usage is idiomatic. Many if not most native speakers would say than him there, and than he would be considered "hypercorrect" nowadays.
Here are two idiomatic ways of making that statement:
Michael Jordan's brother is more athletic than he is.
Michael Jordan's brother is more athletic than him.