Earlier quoted context omitted.
> or does Dropbox actively push any changes to all devices? I may be misunderstanding your question, but it seems to me that this is literally the whole point of the service. Dropbox is a folder that syncs. You change something on one device (one write), it updates everywhere (multiple reads). They do have some tricks to lower their bandwidth usage. AFAIR, if multiple devices are in the same LAN, only one gets synced…
The mobile clients only show you what's there and download on demand, at least that's the default.
(I think a good Linux analogy would be FUSE, things like sshfs.)