Well David... you're going to use the Blend tool to create a surface based on the edges of both the edge of the larger hole and the edge of the extruded surface that sits below.
So you'll end up with a surface that launches off of the original object and lands perfectly with the extruded piece, to put it another way.

Yes, the Blended surface will be trimmed to become the inside 'bowl' of the recess.
The Extrude was just a way to "steer" the course of the Blend surface to its "peeled away" shape.