CAESAR II calculates operating stress in accordance with B31.3 Appendix P when the Appendix P option is activated. You will see this value in the "Code Stress" column in the stress output.
I guess you are asking about the values listed under the "Axial Stress" column in the CAESAR II stress output. These stresses will not include any stress intensification factors. These columns (i.e. axial, hoop, bending, torsion stress etc. and the SIFs) are general calculations and omit special code adjustments. I treat them as just that - general calcs - and do not expect the individual columns to sum up to the "Code Stress" column.
You can test CAESAR II results with a simple one pipe job where you juggle SIFs, tensile & compressive loads and pressure.
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Dave Diehl