The answer is yes, sort of.
I currently have two 32 S&W shell plates in my possession. The diameter of the shell plates are 3.577" and 3.576.
I checked the dimensions of the recess of the progressive's steel base where the shell plate is mounted and got 3.625 +/- .001" on the three progressives I have sitting here. So there is room for the shell plate.
I checked the diameters of a whole bunch of 38 Special Shell plates and they measured 3.618" +/- .003"
I mounted my 32 S&WL tool head (after changing the angle lever cam) on a progressive with the 32 S&W shell plate and cycled a few cases thru the press. The only real problem was at the sizing station. Since the 32 S&W shell plate is smaller than the 38 Special shell plate, and the case is smaller as well, there is a fair amount of slop between the case and edge of the steel base. If you push the case all the way into the shell plate, no problem. If the case is sitting out against the edge of the steel base, you are likely to catch the edge of the case and crush it. A was using a Lifetyme sizing die.
At the primer station, the movement of the primer slide carries the case into the proper position, plus the expander has a pretty good bevel on the end, so that also helps assure the case is in the right position for the primer.
Likewise the mouth of the seating die has a pretty good bevel, or lead in which tends to move the case over to the proper position, so I didn't encounter any problems there with the limited number of cases I cycled.
So while I don't think it's optimum I think you can load 32 S&W on a Progressive. You just have to push the case into the shell plate at the sizing station.
It has been said that Star made Progressives in 32 S&W. I assume Star machined the "rim" of the steel base to the proper size to properly position the cases on those machines.
Bruce