A directory is stored as a linked list of clusters like regular files, and the 32-bit filesize field is irrelevant for a directory, so it theoretically could be as big as the whole volume - just keep adding clusters to the chain.

Filesystem drivers may give up long before then, and access to such a huge directory would be very slow, but there's nothing in the filesystem structures itself that would prevent it. I've written FAT code for an embedded device that I can confidently say would have no problems with large directories, since it'll just keep following the cluster chain to the end.