Yeah all the Z3100/Z3200 models should be able to calibrate and profile with the internal spectrophotometer (an X-Rite i1 according to brochure) through the Colour Centre in HP Utility.
The APS is an odd duck. It came with my Z3100ps GP but I never used it. I thought it was only for monitor profiling and my NEC monitor already had stuff for that so I left it in the box.
But I learned just a year or so ago that the APS also has some extra print profiling options (compared to HP Utility / Colour Centre), including printing and scanning of custom profiling targets. (I finally tried it out to help with some print profiling tests.)
Near as I can tell some of these APS features were more-or-less rolled into the HP Utility for the Z3200 (and HP kind of abandoned the APS as a Z3100-era relic). The HP Utility will show different menu options in Colour Centre depending on which printer models are connected. So on my Z3200ps the Colour Centre shows a Colour Measurement option in the menu whereas it does not for my Z3100ps GP.
A non-PS Z3200 might be missing that option too, but you can easily check. But it's not anything you really need unless you want to get into printing/scanning custom profiling targets instead of using the included ones.
(There is also lurking somewhere on this site a techie thread about "converting" non-ps models to PS

)