General industry practice...
You can log sole man PIC towards FAA requirements, typically the ATP. Regionals will be fine with that, and FAA regs allow it.
For majors (and higher-end non-121 employers), when they ask about your turbine PIC they want actual signed-for-the-airplane PIC, ie the captain/PIC of record. They do not expect to see sole man PIC mixed up in that number. If you read the fine-print, they tend to specify that on their applications.
If it were me, I'd log sole man PIC in it's own separate column... that way you can track it while keeping it separate from your actual in-charge PIC. Sol man is legitimately useful for FAA ratings and IIRC it can also count towards required mins for federal pilot jobs (not so much private sector jobs).