Yes, you can log it. There are several interpretations. I've copied one below.

As has been noted, most (if not all) airlines will NOT count that time as PIC so you'll need a way to remove it easily from your totals when filling out job applications.

That leaves the question of whether or not you should log it. I don't because there's no reason to log it.

Legal Interpretation # 92-46

August 3, 1992

Mr. William Clay Cunningham

Dear Mr. Cunningham:

Thank you for your letter of September 28, 1991, in which you ask
a question about the logging of pilot-in-command (PIC) time when
operating under Part 135 of the Federal Aviation Regulations
(FAR).

Before addressing your question, I would like to first apologize
for the delay in responding to your letter. In recent months, a
large number of priority projects have been assigned to this
division that have prevented us from responding in a more timely
manner to the many requests for interpretations. Mr. Irshad A.
Haqq of my staff recently discussed this situation and the
question raised in your letter with you via telephone. This
letter constitutes our formal reply.

In your letter, you pose the following scenario: under a part
135 operation, the flight crew of a 19 seat deHaviland Twin Otter
(DHC-6-300) consists of a captain and first officer, neither of
whom is required to possess a type rating to act as a flight
crewmember. You then ask whether the first officer may log PIC
time for the period during which he is the sole manipulator of
the controls of the aircraft. You also explain that you have
received conflicting answers from local FAA personnel to whom you
have posed this question.

The answer to your question is yes. Under Section 61.51(c)(2) of
the FAR, the first officer may log as PIC time that time during
which he is the sole manipulator of the controls of the aircraft.
In fact, both the captain, assuming he is the designated PIC
required under Section 135.109, and the first officer may
simultaneously log as PIC time that time during which the first
officer is the sole manipulator of the controls.

We recently rendered an interpretation encompassing the issue you
raise as well as other questions related to the logging of PIC
time under the FAR. A copy of that June 25, interpretation
addressed to Mr. Dallas Butler is enclosed for your reference and
convenience. The sections of the FAR that are pertinent to this
issue are cited in that letter.

We hope this satisfactorily answers your question.

Sincerely,


/s/ Donald P. Byrne
Assistant Chief Counsel
Regulations Division