The answer to this question depends on a designer or fabricators understanding of Part UG-22 "Loadings" in ASME Section VIII, Div 1. If you carefully read thru this section, paragraph (b) sums it up. This paragraph requires a designer to take into account the weight of the vessel and contents including additional pressure from static head.
In some cases, the loadings of UG-22 could be negligible in comparison to internal pressure.
The part on determining minimum wall thickness under internal pressure (UG-27) also requires the designer to take into account loadings from UG-22.