There is indeed an account of a Turkish Sultan’s brother being murdered in New Orleans, but that dates over a century after the fact, so cannot be entirely relied upon (even though it appears that the unknown DC Comics writer copied the tale almost verbatim from that text). Indeed, there are no other records of such an event occuring at any time in New Orleans’ history, as far as I can tell.
As with all tales of this nature, it has grown in the telling; this exiled Turkish royal is now said to have had wild orgies every night; 37 men, women & children were murdered along with him, and the crime was only discovered after blood trickled down the steps leading to the front door. Given that DC was more of a kid-friendly publisher at the time, omitting such details is quite understandable.
This makes the tale even more dubious, especially when we consider that the house in question, known as either the Gardette-LePrete mansion or (of course) The Sultan’s Palace, was built almost 110 years before this grisly nonsense was said to have taken place. The current owners, who have turned it into six aparments, have pooh-poohed the tale, but do say that it appears to be haunted. Of course, saying a house in New Orleans has ghosts is like saying every square inch in Nottingham has a connection to Robin Hood; it’s just what people say to tourists.
The house did at one point have a date tree (and might still do – any sources I’ve found are vague on the issue) but given that a Capuchin friar once freely distributed seeds from his own date palm tree to the people of New Orleans, I think we can attribute something other than murderous Turks.