It should, since the approved procedure already contains the steps, hazards and controls that engineering and operations agreed on, and generating a new JSA from scratch throws all of that away. Starting from the SOP means the JSA reflects the approved way of doing the work, and the crew’s time goes into what is specific to today rather than rewriting the basics.
This only works when procedures are stored as structured steps rather than PDFs, since the permit needs to pull specific steps and their hazards rather than attach a whole document. It is also a good example of why procedures and permits belong in the same system, because the permit and the procedure describe the same job and should not be written twice.