Is there any way to add a table to an existing diagram and ONLY show links to the tables in the diagram?
If I understand the question correctly, I'll say no, not that I'm aware of... at least, not for the Database Diagrammer. There, the DB Diagrammer will try to find any table/view in the database that is directly linked to the table you drag into the diagram palette.
However, if you're talking about the Query Builder diagram, and if there is referential integrity defined between the new table you drag and the tables already present on the palette, then that new table will be joined automatically to any of its relations already present in the palette (and only those tables present, even though there may be other tables in the database that are related to the newly added table.
Hope that clarifies things.