I would like to use to syncthing to sync my ubuntu desktop (always running) and my ubuntu notebook. Everything I do on the notebook should be changed on the desktop and the other way around.
The desktop has additional USB drives mounted which I would not like to sync.
No, Syncthing will not be of any help. Even if you managed to ignore all the parts that should not be synchronized (/proc as mentioned, every little thing in /etc that is system specific, log files that should be system specific, pid, status and lock files that are system specific, and so on), Syncthing does not synchronize user and group ownership of files.