So I just went ahead and tried it. And yes, inside the Xbox 360 S Hard Drive enclosure is a standard 2.5 inch hard drive that can then be inserted into the original Xbox 360 hard drive enclosure.
Downside is that the S enclosure is glued together, so getting the drive out is very destructive to the casing. If you have a heat gun maybe you could soften the glue and take it appart without damaging the case, but I do not.
Anyway, short version. If you, like me, want to upgrade to the latest and greatest Xbox 360 hard drive size, have the old model Xbox 360, don't have the means/patience/skill to hack your own disk, and require the use of the original Xbox emulator (the aftermarket drives I looked at do not have this) then yes, you can use the Xbox S Hard Drive in your original Model 360. Just follow the previously posted guide for dissassembly of the hard drive enclosure, and take care when cracking open the S enclosure.