I don't know about Dropbox (I don't even know what it is exactly) but with Microsoft Live Mesh it works great. I'm the one managing the books in our houshold and my wife is only reading them.
My Calibre folder is in the Mesh. Ik can do anything I want there on my PC, laptop or anywhere in the world on any PC. My wife has only read access on anything she uses.
In this way she always has the latest version of the library and cannot by accident delete or change books.