I'm wondering whether the emphasis on "complete" in the original post is meant to imply that perhaps only the weld seams, but not the unwelded areas, be PWHT. If that is the intent, then I suspect that after a thorough discussion with the client / end user, then you may find that some areas of the vessel may be exempt from PWHT. Actually, something like studs and manway covers are likely not considered a part of the "complete" vessel in many cases.
Now, if one is to envision a PHWT of the welds only, then the state of stress in the vessel would be quite interesting. Certainly worthy of an FEA to evaluate the stresses during PWHT. And said FEA would likely indicate that the PHWT will leave yield level residual stresses when completed. In other words, such a proposal is likely to be completely impractical for the vast majority of cases.