Yes, you can do the same in VMware. However my scenario is different:
Host OS only uses Dropbox to sync VMware machines. One Debian VM syncs all Dropbox data (except the VMware machines) and provides that Dropbox folder to the LAN via SMB/FTP. Having Dropbox on each server/workstation creates a mess, so we switched to a centralized solution with SMB/FTP and use 1 Dropbox instance as a background cloud sync.
The benefit is that the VMware host can crash, and I can quickly deploy the Dropbox VM to a new server and do not need to resync everything. Its much faster to manage a LAN this way.