This may seem like an easy answer at first: no. The generally accepted rule within part 121 is that a designated SIC never logs PIC time, whether they are a FO, Captain, or Check Airman. That's the answer I'm getting from asking around my operation as well, but I'm not convinced it's accurate.
In the 1999-Carpenter legal interpretation, the FAA wrote the following (italics added for emphasis):
Dear Mr. Carpenter:
[ ... ]
Lastly, you present the following scenario: under a Part 121 operation the air carrier has designated a pilot and a copilot as required by FAR 121.385(c). The pilot is the authorized PIC and the copilot is the authorized SIC. The PIC is also the company check airman. During the course of the flight, the SIC is the sole manipulator of the controls for the flight. Additionally, he has passed the competency checks required for Part 121 operations, at least as SIC. You ask whether the SIC can log PIC time for that portion of the flight in which he is the sole manipulator of the controls for the flight. The answer is yes. There is a distinction between acting as pilot in command and logging of pilot in command time. "Pilot in command," as defined in FAR 1.1, "means the pilot responsible for the operation and safety of an aircraft during flight time ....
While it is not possible for two pilots to act as PIC simultaneously, it is possible for two pilots to log PIC flight time simultaneously. If the pilot is designated as PIC by the certificate holder, as required by FAR 121.385(c), that person is PIC for the entire flight, no matter who is actually manipulating the controls of the aircraft, because that pilot is responsible for the safety and operation of the aircraft. The pilot who is the sole manipulator of the controls of the aircraft for which the pilot is rated may also log that flight as PIC.
It seems to me that the key here is the application of 61.51 (e), a regulation governing the logging of pilot experience, to a 121 operation which requires a designation as PIC/SIC for legal responsibility for the safety of the flight. Under part 61.51 (e), the sole manipulator of flight controls may log PIC time without being the designated PIC, just like a flight instructor and private pilot seeking a higher rating. The CFI is the designated PIC in that scenario, but the PPL, who is sole manipulator of the flight controls (usually), is also logging PIC time.
To me it looks as though there's an industry-wide misunderstanding of how the FAA intended the regulation to be applied, but I think there's probably a more likely explanation - I'm missing some piece of the puzzle.
So my question is this: what is your interpretation of what I've written here? Has Carpenter-1999 been superseded by a more recent legal interpretation, was the FAA wrong in their explanation, or do we as a pilot group widely misinterpret the FARs as they apply to logging PIC time under a 121 operation?