Given that Haiti is practically at its knees without a functioning government, if their president requests that the United States occupy and run the country (at least temporarily) until it gets back on its feet, should we do so?
No. The last time the US occupied Haiti you indirectly encouraged the rise of Duvalier just like you indirectly encouraged the rise of Pol Pot in Cambodia by bombing the sh**t out of the country and supporting a corrupt, venal puppet.
Foreign occupation is a bad idea. Anywhere. You cause more sh**t than any incompetent local loser can.