Well they did and they didn't. They shared a similar culture as they were from Africa, but a lot of times it stopped there. Slaves and workers were brought from many parts of Africa with various languages and cultures intermixed. On top of that, the slave work in Haiti was so brutal, that it had a much higher mortality rate then places like the U.S. This meant that new slaves were consistently being brought to replace the dead. This prevented a strong local slave culture developing like it did in the U.S.

This is just very general as I am not sure what time period you are asking about. A lot of other factors including wars with European powers have destabilized Haitai over history.