On the PNA Vector Network Analyzer Family Is it possible to save a Touchstone (SnP) file with unwrapped phase?

Yes. The PNA Family of Vector Network Analyzers can save Touchstone (SnP) files with the phase information as unwrapped phase. To achieve unwrapped phase in a Touchstone file save perform the following:

Alter the display format of the active S-parameter to unwrapped phase;
Within the Define Data Saves dialogue window under the SnP Format selection choose the Auto radio button.
The resultant Touchstone (SnP) file will be saved as linear magnitude and unwrapped phase format.

Additional Notes:

Below are results for a 3’ cable under test. A full 2-port Ecal calibration was performed from 1.0 GHz to 2.0 GHz with 101 points. All traces are set to measure S21.

Trace 1, Tr 1, is S21 unwrapped phase;
Trace 2, Tr 2, is S21 wrapped phase;
Trace 3, Tr 3, is S21 group delay. The positive group delay in Tr 3 serves as a method of confirming no aliasing exists due to an inadequate number of sweep points.

The excerpt below is of the Touchstone S2P file save while Tr 1, unwrapped phase format, is the selected active trace. Highlighted entry correlates to the S21 unwrapped phase marker at 1.500GHz on Tr 1.

!Keysight Technologies,N5242A,MY52021989,A.09.90.02
!Keysight N5242A: A.09.90.02
!Date: Monday, July 22, 2013 10:33:51
!Correction: S11(Full 2 Port(1,2))
!S21(Full 2 Port(1,2))
!S12(Full 2 Port(1,2))
!S22(Full 2 Port(1,2))
!S2P File: Measurements: S11, S21, S12, S22:
# Hz S MA R 50
1000000000 0.00182216 140.46735 0.97429383 134.07173 0.97405386 134.05788 0.0050454582 -120.71554
1010000000 0.0032124652 91.299805 0.97419584 121.02003 0.974033 121.00049 0.00011965834 -107.46384
...
...
1500000000 0.022686627 -783.6239 0.96601903 -518.46204 0.96537387 -518.48163 0.018601269 -64.083313
...
...
1990000000 0.014492352 -1607.0535 0.96125519 -1157.7521 0.96084422 -1157.767 0.023459071 -146.25398
2000000000 0.01027567 -1630.2699 0.96131885 -1170.8003 0.96079588 -1170.8195 0.019408535 -158.19107

The excerpt below is of the Touchstone S2P file save while Tr 2, wrapped phase, is the selected active trace. Highlighted entry correlates to the S21 wrapped phase marker at 1.500GHz on Tr 2.

!Keysight Technologies,N5242A,MY52021989,A.09.90.02
!Keysight N5242A: A.09.90.02
!Date: Monday, July 22, 2013 10:34:09
!Correction: S11(Full 2 Port(1,2))
!S21(Full 2 Port(1,2))
!S12(Full 2 Port(1,2))
!S22(Full 2 Port(1,2))
!S2P File: Measurements: S11, S21, S12, S22:
# Hz S MA R 50
1000000000 0.00182216 140.46735 0.97429383 134.07173 0.97405386 134.05788 0.0050454582 -120.71554
1010000000 0.0032124652 91.299805 0.97419584 121.02003 0.974033 121.00049 0.00011965834 -107.46384
...
...
1500000000 0.022686627 -63.62389 0.96601903 -158.46199 0.96537387 -158.4816 0.018601269 -64.083313
...
...
1990000000 0.014492352 -167.05351 0.96125519 -77.751999 0.96084422 -77.766945 0.023459071 -146.25398
2000000000 0.01027567 169.73019 0.96131885 -90.800278 0.96079588 -90.819427 0.019408535 -158.19107