|This is what Dropbox says about using an external drive|
"You can move your Dropbox folder to any location on your hard drive using the Dropbox desktop application. If you decide to move the folder, we strongly recommend choosing a location on the same hard drive as your operating system. Dropbox won't work correctly should the Dropbox folder ever become inaccessible.
Please note that Dropbox is not compatible with network filesystems. The problem is that network file systems do not send messages when files change. When Dropbox first starts it will do a deep file scan and will detect changes and sync them. However, during normal operation, Dropbox waits for "file update events" and only physically connected drives send these events. Take this into consideration when choosing a new location for Dropbox."