O Dropbox LAN Sync é o que você deseja ativar.
Citações do link
LAN sync is a Dropbox feature that speeds syncing dramatically when the file exists on your Local Area Network (LAN).
What does that mean exactly? Well, when you add a file to your computer's Dropbox, the file is then synced with Dropbox servers. Dropbox will then initiate the syncing process as soon as it determines a change has been made to the file. All linked computers and shared folders will then download any new version of the file. With LAN syncing, Dropbox will look for the new file on your Local Area Network first, bypassing the need to download the file from Dropbox servers, thus speeding up the syncing process considerably.
LAN sync is an extra advantage for use in locations where computers are networked together over the same router or other local area network.