Jim Garrison seemed to think so. Here is a memo he wrote in February, 1968.
Here are two photos of the Old Post Office Building:
You can see that the Post Office is right across the street from Reily Coffee, where Oswald worked for two months in 1963. In the first photo, you can see Mancuso's Cafe. where Banister, and many Cubans hung out in the early 1960s..
Garrison mentioned the Post Office Building again when Kerry Thornley was indicted for perjury.
But, why wouldn't Thornley have a post office box in that building? After all, it was only a block or two from Thornley's apartment. His friend Greg Hill wrote, "nearly every writer in the French Quarter had a box in that post office, since publisher's checks sent to home mailboxes were notoriously subject to being ripped off by desperate junkies."
Garrison never gave up on the Post Office building, and he wrote about it in his book, On The Trail of The Assassins. To learn the truth about Kerry Thornley, and why he was indicted by Garrison, read my book, On The Trail of Delusion.