If Dropbox isn't allowing you to 'see' your folder structure, isn't that a Dropbox or OS issue? I'm not sure how Premiere is supposed to sort that out. Unless I'm misunderstanding something from your post.
My partner and I work together constantly ... he's in Cape Town, I'm in Oregon, and we run 'regular' projects, Team Projects, and even a Production via LucidLink's service with the storage on Amazon S3 servers in London.
LucidLink does two things that are WAY above any other service: it incredibly intelligently uses "packets" to move data in usable forms, and utilizes a "virtual drive" on each computer for easy 'apparent' file management.
Mo and I can be on a WhatsApp phone call ... he tells me he's copying a folder of media from his Mac to a folder in our filespace. Within a couple seconds, I see the folder appear on my LucidLink "drive" tree. Shortly followed by the files.
Which haven't finished uploading to London yet, but I'm already importing them into Premiere on my machine and adding the clips to sequences! Because the bits needed are sent as they would be used.
We've been rather stunned ... and use that service all the time now.