Are items in the collection still searchable if they are not viewable by the public?

Yes.  All text items in the collection will be full-text searchable.  If your items have embargoes which limit access, users will still be able to find the items, but they will only be able to view the metadata records (descriptions).  For items limited to the UNT community, public users will be able to see only the metadata records but users affiliated with UNT will be able to sign in with their EUIDs to view the full text.