You can make it so a user can create a thread, but only staff can see it; however, I don't think it's possible to do what you want, not without an add-on, at least.
Yes, under node permissions for the forum you want the user to post in revoke "View threads by others:" then Allow "View threads by others:" for staff.
Yes, under node permissions for the forum you want the user to post in revoke "View threads by others:" then Allow "View threads by others:" for staff.
We do this and it is very useful for staff contact. We also direct reports to this forum so staff can discuss the report with the member who made the report.
We do this for members to question the actions of Moderators somewhere where only the senior team can see them. We use a separate forum (node) and have the permissions set up as described by @Steve F - meaning either specific personnel (individual permissions) or (in our case) our seniors' secondary usergroup can see all of the node's contents, and the thread originator can see "his" threads only. Everyone else sees an empty node. Works perfectly.