That's an interesting idea. In theory it should, since each one of the folders/contents are on your computer as well as online. But it might be tricky dealing with different libraries on different computers, unless of course you plan to keep your media files in Dropbox too.
I think it might be worth exploring. Dropbox probably isn't used widely enough that many people here (if any) have tried it, so you may not get any responses here. I do use it, but it never occurred to me to install MC into it.
-Chris