Does mounting an EF vs an EF-S lens produce the same results on a camera body that has an APS-C frame size?

Yes. They will produce the same results, assuming all the same settings, and similar optical performance between the two lenses, and 100% accuracy in the actual focal length of the lens as reported (manufacturers have been known to fudge the number). Theoretically, an EF 50/1.8 and an EF-S 50/1.8 with identical optical performance and identical aperture settings would produce identical images with identical exposure settings and depth of field when mounted on the same body.

... aren't the EF-S range of lenses physically closer to the sensor whereby the focal length IS actually shorter?

No. You're assuming that registration distance (i.e., how far the lens is held from the image plane) affects the focal length. It doesn't. Focal length is an internal measurement and physical property of the lens itself. Changing how far away from the image plane it sits or the size of the image plane behind it doesn't affect the lens's focal length at all.

In addition, as Michael Clark points out in a comment, the registration distance for EF-S and EF lenses is identical: 44mm. That the "S" in EF-S stands for "short", and the back element can protrude farther than with EF lenses doesn't mean that the lens overall is held closer to the image plane for crop bodies, but that because the sensor is smaller, the mirror is also smaller, which means as it swings up, there's a larger clearance at the back end of the lens, so EF-S rear elements can stick farther out than the rear elements of EF lenses can on a full-frame body without hitting the mirror.

... If EF-S lenses (as a whole unit) are shorter and have a shorter back focus plane, wouldn't that make the FOV wider (ergo not producing the same image)?

Think about moving a projector closer to the screen. Does the image get bigger or smaller? Sharper or fuzzier? Because the sensor area that has to be covered by the lens's projected image circle is smaller and the lens can therefore produce a smaller, sharper image with less optical correction.