you want to have a course in your Moodle website and the same course in your MoodleBox. You will get no problem if your course on the MoodleBox uses a special activity which is only on the MoodleBox. This activity should have an end date. After this date you backup this special activity on your MoodleBox included all users and all grades. You restore it into your course in your Moodle website.
You need to be manager or admin in both platforms. All course users should be the same on both platforms with the same usernames and the same email addresses. No, the process will not run automatically.
Yes, I still have the same problem with my teachers workshops. https://machmitnetz.de/course/view.php?id=182#section-2 . When the teachers are using my MoodleBox with the iBeacons outside in the wood far away from mobile data they will find all their materials and activities on the MoodleBox. They should not use anything else from the internet and they should send their ideas and activities (assignment, feedback, choice, database, glossary) to the MoodleBox. Yes, the results are copied to a workshop course on the Moodle website https://machmitnetz.de so the teachers can see their results also when the workshop is over.