Fork for integrated headset work with regular headset?
 

Can they interchange or are they mutually exclusive?

Looking at the full Carbon cross fork from PBK.

Not sure about the PBK fork, but I know the Ritchey Carbon Cross fork I have was advertised for use with either type of headset.

It might look goofy but so long as the crown race diameter isn't some oddball diameter it should work.

yeah, not sure if it's merely a looks thing or if its an actual clearance issue.

The type of headset required is determined by the frame (specifically, the head tube), not the fork. All threadless forks work with all threadless headsets, assuming you have the right diameter steer tube (1-1/8' or 1"). As someone else mentioned, the fork crown may or may not match up with the head tube, but that's aesthetic, not functional.

There are two (I believe) crown diameter dimensions, but I can't remember off hand what they are.

Yup.