HornResp Question - S1 Visual vs Area

This may be obvious but I need someone to clarify if possible. Using a tool like HornResp, I'm trying to grasp how S1 (area of the entrypoint to a horn) relates to Sd (area of the speaker cone) when the two are different shapes.

Good example is an Altec 816, where the business end of the driver+horn looks like a sideways Underground sign. Sd of a 15" driver is somewhere around 1000cm2. Drawings of the Altec 816 show that the rectangular horn entry S1 is 21"x8", so about 1084cm2, so pretty close in area. Except, visually there is some dead space for both components - part of the driver's Sd area is blocked behind the horn entry, and part of the horn's S1 area is made up of inert motorboard.

Does the shape of the horn entry and its relationship to the driver cone have any impact on the effective S1? The obvious answer seems to be no, but the configuration of the Altec 816 - where a meaningful amount of S1 area is some meaningful distance from the actual driver - has me doubting. Thanks in advance!