Hi Burr, yes if all the underlying surfaces have matching control points at edges where they join up, it's then still possible to turn on control points for the joined object.

In the more general case where the joined edges are arbitrary trim edges rather than a "natural edge" of the underlying surface then you won't get control points for the joined object but in that case you can still get them by using Edit > Separate on it to break it apart into unjoined independent surfaces.

For others reading this, there is some more information on surface control points and how "underlying surfaces" work in this FAQ answer here:
http://moi3d.com/wiki/FAQ#Q:_Why_does_show_points_work_for_some_objects_but_not_others.3F

- Michael