Sure--- from Belgium it would take longer. I maybe off a couple of days, but slave communication was notorious for leaping hundreds of miles in just days. In 1811, there were overland routes, river routes, shipping lanes to Charleston. I have no doubt this uprising was known very early across the South. A week would be about right for a swift sailing vessel from New Orleans to Savannah or maybe Charleston. Average speed of Baltimore Clipper- 8 knots--- that's about 220 miles a day--- 1600 miles---- is about 7 days.
"We should also be aware that none of the states along the Gulf of Mexico existed prior to 1812."
That doesn't mean the area wasn't inhabited.
Like I said, I don't believe Turner's Revolt alone turned the attitudes of Southerners against free blacks and manumission in the 1830s--- And more important increased pro-slavery attitudes.