In my opinion this should be considered a secondary stress and the stress range resulting from the combination of this axial stress and secondary bending & torsion should be compared with Sa. This is my interpretation of B31.3 para 319.2.3-c.
For this purpose I would enforce "Add F/A in Stresses" directive in Configuration-->SIF & Stresses. Caesar will, however, not consider the stress intensification for the axial stress component.
Better approach will be to refer Appendix "P" which addresses the combination of axial stress with other components and also the SIFs for axial stresses.

If this axial stress component is considered primary (non limiting) stress then this alone will not be compared with S, rather its combination with other primary stresses (SL of B31.3) will have to be compared with S. In certain cases this combination will be approaching or exceeding the limit and may dictate basic design changes e.g change in wall thickness etc.