Question re syncing only some databases

Suppose I have databases A, B, C on machine 1. Now I sync A, B and the global Inbox to machine 2 (not database C!).

Now, what is supposed to happen if I

• add a document (say xyz.pdf) to the global inbox on machine 2
• later (i.e. after a sync) I move this document to database C on machine 1

Should the document stay in the global inbox on machine 2 (thus the inboxes on the two machines being out of sync)? Should it disappear from the inbox on machine 2 (where to – thin air?)