Yes.  

Regarding logging PIC time, 14 CFR § 61.51(e) states in part:

> (1) A sport, recreational, private, commercial, or airline transport
> pilot may log pilot in command flight time for flights-
> 
> (i) Except when logging flight time under § 61.159(c), **when the pilot
> is the sole manipulator of the controls of an aircraft for which the
> pilot is rated**, or has sport pilot privileges for that category and
> class of aircraft, if the aircraft class rating is appropriate;
> 
> (ii) When the pilot is the sole occupant in the aircraft;
> 
> (iii) When the pilot, except for a holder of a sport or recreational
> pilot certificate, acts as pilot in command of an aircraft for which
> more than one pilot is required under the type certification of the
> aircraft or the regulations under which the flight is conducted; or

You really don't need to go any further than that.  

You cannot "perform the duties" or "act as PIC" without a current medical certificate, (stated elsewhere in the regulations).  The FAA breaks PIC duties out separately from "sole manipulator" and your friend must be that.  But if you are a rated pilot flying the airplane you can log the time while you are sole manipulator.