For half-pipe jackets in Appendix EE, does the rated maximum pressure P take into acout the external pressure placed on the shell itself via the K factor? Meaning if my P value is satisfactory to me based on my K value, do I not need to do any further investigation of the shell for external pressure loadings?

Under normal circumstances, a cylindrical shell convex to pressure is analysed per UG-28 where the graphs in ASME Section II - Part D must be used. However, the length (L) of the shell under one of the half pipes is very short compared to its diameter (Do). Under these circumstances the short length can be treated as a 'beam'. It is interested to note that in the German AD (Merblatter or 2000) code, this is shown in detail.

If the half pipe system complies with Appendix EE, it takes into account the external pressure on the cylindrical shell.

Therefore, no further investigation is needed.