I just checked the fit of lens-side K mount on a Pentax body with autofocus mount. Seemingly not only the automatic diaphragm, but also open aperture metering works (I'm just looking at the actuators).
The lens-side mount is a Adaptall-2 mount and Tamron state that for an AF camera one needs instead the KA mount (of course not transferring AF information).
Yes, automatic diaphragm and open aperture metering work with regular K-mount lenses. So, does aperture-priority auto mode. KA mount adds support for shutter priority and program modes. KAF adds AF support.