Does the revenge in this play satisfy a human longing or does it just lead to more dead bodies at the end of the play?
We might consider revising the question somewhat. Whose "human longing" are we considering here? Hamlet's? The reader's? Shakespeare's? Claudius's? etc? In fact, in Hamlet's case, it might not be an "or" question.
If it's the reader of who we speak, then the revenge becomes a sublime thing and yes, it does satisfy a human longing to "right the balance" and bring things into a natural Shakespearean order. As readers we participate in all of Hamlet's human indecisions, his angst, anger, frustration, then finally are cathardically "purged" of any revengeful thoughts with Claudius's death.
If it's Hamlet of who we speak then, yes again. It is a human longing that Hamlet seeks and attains his revenge. The death of his father and the inversion of the traditonal order and process of accomplishing things is ruined in Denmark. Hamlet as a human longs for order and longs to revenge his father's untimely death. Unfortunately, in Hamlet's case, satisfying this human longing means also tragically loading up the stage with bodies at the end of the play.
As a reader you do follow Hamlet through his entire spectrum of emotions throughout the play. This causes you to be invested in his character. One way this question can be interpreted is to ask if the reader's longing for justice has been satisfied. From the very beginning of the play the death of King Hamlet was unjust. The viewer of the play feels that a great wrong has occured and wants there to be justice. As revenge is sought out we find ourselves rooting for Hamlet, but the twisted nature of the play also causes us to begin to doubt his intentions and plan.
Or look at the death of Ophelia. With that death being caused by the deception of Hamlet pretending he has gone crazy, we begin to see that he is not merely seeking revenge for his father's death, but he is also causing great havoc and trauma in the lives of everyone around him.
Then again, the death of his mother may be seen as gratifying to the human desire for revenge because his mother remains so obstinantly naive to the murder of her husband.
In the end, even his own death may seem to Hamlet and the viewer a fulfillment of revenge. We may say that Hamlet deserved to die for causing innocents to die.
These are some ideas to throw around as you narrow that question.
Not only in Hamlet, but revenge itself, throughout drama and, for that matter, human history, satisfies victim's emotions AND leads to dead bodies. Finding better ways to right wrongs appears to be an eternal human struggle.