The original question is a good one. Instrument training (either with a CFII or SP) is loggable as PIC in FAR terms if you are rated at least as a PPL in that aircraft. With a CFII, it is also dual.
This is true under the hood in VMC, or in IMC with an instructor. This is a little bit counter-intuitive since you are not rated for the IMC flight condition, but that's how it is generally done.
Actually there are two phases of your career as far as PIC goes, and the real-world definition of PIC is different between the two.
At the entry-level, including regionals, they will generally accept any FAR-legal PIC towards their required totals.
When you apply to majors, they generally want to break out dual received, dual given, safety pilot, etc. These times will still be counted, but seperately. Probably safe to safe the majors will not care about exactly how you logged PIC while a PPL, as long as it was not fruadulent. Ultimately, for your PIC total they are interested in time in which YOU signed for the airplane and flew it...this is the gold standard.
Folks who come up with schemes to log PIC when they were not the CA usually find out that it doesn't work...interviewers can sniff that out. Kind of like the FAR provision to apply some SIC while "fulfilling the duties of PIC" to the PIC mins for an ATP...that time would still be SIC, not PIC. It can be used towards an ATP, but not for anything else.