At least with the first PS4 model it works, so I see no reason why it shouldn't work with the Pro. The limitation is the use of one of the rare USB ports of the PS and the fact that the volume cannot be adjusted directly on the headset (although the control element would be available - but it only works on the PC). Insignificant but nevertheless worth mentioning: the various settings such as colour adjustment etc. can only be changed on the PC and cannot be adapted on the PS.
I hope I was able to answer your question with this.
