Works for me on a local system.
The Drop Box permissions are set to
/bin/ls -dleO@ Drop\ Box
drwx-wx-wx+ 3 testing staff - 96 Apr 13 21:24 Drop Box
0: group:everyone deny delete
1: user:testing allow list,add_file,search,delete,add_subdirectory,delete_child,readattr,writeattr,readextattr,writeextattr,readsecurity,writesecurity,chown,file_inherit,directory_inherit
I can drag and drop a folder with files and subfolders into the ./Public/Drop Box, and it copies over all the files, and subdirectories with their files.
If your permissions match, then maybe it is an SMB thing.
I know years ago, when I worked on a Digital Equipment Corporation AppleShare Protocol compatible OpenVMS file server, we supported Drop Box behavior. This was over the AFP protocol, not SMB, and at the time, Apple also support Drop Box behavior from another Mac (I often did protocol sniffing to make sure our file server behaved the same as Mac to Mac file sharing with respect to protocol messages.