The problem with your technique is that Intersect Faces with always creates Edges only in the currently active edit context. In your case, that was the model as a whole, so the new Edges did not actually cut any Faces inside either of the Components. When you explode, that is not enough to cause those Edges to cut the Faces.
What you need to do is to get all the geometry into a single context before you do the intersection. For example, open the plane for edit, select the face, copy or cut it, then close that component. Next open the pipe component, do edit->paste in place to deposit a copy of the plane, and then do the intersection. Now, since the new edges are in the same context as the pipe’s geometry the faces will be cut.