May an uncertificated pilot log non-PIC flight time for future certification?
Your friend can't log any time because he isn't licensed and qualified to fly the aircraft and assuming that you aren't a CFI then he isn't receiving training either. He's just a passenger, although if he wants to record the time for his own purposes that's fine, it just doesn't count for anything as far as the FAA's concerned.

First, 14 CFR 1.1 says that flight time is time acting as a pilot, not just time in an aircraft:


  Flight time means:  
  
  (1) Pilot time that commences when an aircraft moves under its own
  power for the purpose of flight and ends when the aircraft comes to
  rest after landing;


So your friend needs to log time as a pilot. Obviously without a certificate there's no way to log PIC or SIC time, so that leaves training time. The regulations for that are in 14 CFR 61.51 (my emphasis).


  (h) Logging training time. (1) A person may log training time when
  that person receives training from an authorized instructor in an
  aircraft, flight simulator, or flight training device.