I'm trying to add (boolean) an open surface that intersects the solid body. Attached is a very simplified example SW part. In the part I'm working on, it's much more complicated.

This is possible in Solid Edge as long as the surface intersects the body (leaves no gaps) and doesn't extend past the body.

As you can see in the below example that I imported into Solid Edge from SolidWorks, Solid Edge is able to combine the surface with the body with a single feature (Boolean 1). It will work with much more complicated shapes as long as zero manifold is avoided.

Is there an equivalent way of doing this in SolidWorks (2012)?