It's one of the great Creation Myths of New Orleans Voodoo: plantation owners fleeing the Haitian Revolution brought their slaves to the Louisiana Territory, thereby establishing Vodou in and around New Orleans. Like most myths, it has attracted a number of skeptics who point out that there is no evidence of a survival of Haitian customs in the New World before the Duvalier-era diaspora.
It's true that we don't see assons, dwapo lwa, or some of the other items we've come to associate with Haitian Vodou in traditional New Orleans practices. (They are part of the "New Wave" of NO Voodoo, which began in the 1970s and persists to this day). However, that's not necessarily evidence against an NO/Haiti connection. What we call "Haitian Vodou" or "Orthodox Vodou" became popular during the early part of the 20th century, as growing urbanization drew many Haitian farmers off their land and away from their ancestral and village practices.
More damning are the numerous laws against importing slaves from the French Antilles into North America. At this time the slaveholding states were in terrified that the Saint-Domingue revolution would spread throughout the Americas. As early as 1782 there were laws against bringing in slaves from the French Antilles: they had a reputation for being surly and seditious. (Given the conditions on Saint-Domingue and other sugar-producing colonies, who could blame them?!) By 1791 there were searches at most ports to ensure that no one imported Saint-Domingue slaves -- and the Saint-Domingue uprising.
There may have been a few Domingan slaves brought to New Orleans, since it was pretty well-known even then as a smuggling hub. But they were few and far between: as in the rest of the United States, the majority of slaves were from the Kongo regions of central and southern Africa. Kongo practices form the major African influence on both Hoodoo and New Orleans Voodoo. The veneration of the dead, mojo hands, and homage to "La Grande Zombi" (the great Nsambi, or spirit) among others, can all be traced to the Kongo. And of course we have the clearing in the Tremé neighborhood where slaves and free blacks would gather on Sundays to sell their wares and dance, the famous "Congo Square."
But if the Domingans did not bring Haitian Vodou with them, they helped create the conditions in which New Orleans Voodoo was born. They provided a French-speaking and Catholic bulwark against the flood of Anglophone Protestants. This helped to ensure that many folk practices in the city would have a Catholic flavor, as opposed to the Protestant-inspired Hoodoo found in most of the south. They also brought with them a three-caste system of whites, blacks, and mixed-race "people of color." Many Domingan refugees were wealthy, educated gens du coleur who helped establish New Orleans Creole culture: others were free blacks who established themselves as tradesmen and skilled artisans. And they brought with them a culture where interaction between the races was far more common than in the more rigidly segregated Anglophone regions.
All this was instrumental in forming the culture which gave us the folk customs of New Orleans. So while there may not be a direct lineage between the mamalois and papalois of the bayou and the practitioners in Port-au-Prince, there's no question that New Orleans culture owes an immense debt to the Haitian Revolution.