You may be able to get close, depending on your partitioning.
You would want to section off things like:
Onto partitions that did not get synced, as those contain information that might get fiddly being shared between two+ physical machines.
/boot may or may not be a problem as well, that would be a point I'd test to see how it worked out.
You would DEFINITELY want to keep your
network adapter configs separated, which differs based on distribution otherwise I would list it specifically.
All in all though, You may run into random compilation vs hardware issues for certain bits of software that care about what it was compiled on, which could lead you to bigger headaches in the long run.
Depending on what you are using the system for though you would probably achieve your goal more or less by synching specific things such as:
The important thing if doing a partial sync would be to determine certain practices, such as where new programs get installed.
Another option which is granted a bit more nutty, would be to set up each system as a
salt-master server that is also its own minion, then share your
salt states between drop box, and use
salt states as a way of managing your system, so instead of installing a package directly, setup a
salt state to install it, and run the salt state. Then each boot once
dropbox files have
synced, you could let
salt then go through and sync your system to the newest states that you have put in place.
One issue overall you should keep in mind is that dropbox syncing is not immediate, so a system would have to boot before it got the latest files, some files are only loaded on
system boot, so certain config files if you were managing the ENTIRE OS via
dropbox, would not match up with other things that have been synced, which could cause system instability.