Can a non multi-engine rated pilot get a complex endorsement in a multi-engine aircraft?
If the airplane meets the definition, which almost all multi-engine pistons will, then you can get your complex endorsement. There is even one training center that advertises getting your multi and complex at the same time.


  §61.1   Applicability and definitions.
  
  Complex airplane means an airplane that has a retractable landing
  gear, flaps, and a controllable pitch propeller, including airplanes
  equipped with an engine control system consisting of a digital
  computer and associated accessories for controlling the engine and
  propeller, such as a full authority digital engine control; or, in the
  case of a seaplane, flaps and a controllable pitch propeller,
  including seaplanes equipped with an engine control system consisting
  of a digital computer and associated accessories for controlling the
  engine and propeller, such as a full authority digital engine control.





  §61.31   Type rating requirements, additional training, and
  authorization requirements.
  
  (e) Additional training required for operating complex airplanes. (1)
  Except as provided in paragraph (e)(2) of this section, no person may
  act as pilot in command of a complex airplane, unless the person has—
  
  (i) Received and logged ground and flight training from an authorized
  instructor in a complex airplane, or in a full flight simulator or
  flight training device that is representative of a complex airplane,
  and has been found proficient in the operation and systems of the
  airplane; and
  
  (ii) Received a one-time endorsement in the pilot's logbook from an
  authorized instructor who certifies the person is proficient to
  operate a complex airplane.





  Complex Airplane Endorsement
  
  Learn to fly aircraft with retractable landing gear, controllable
  flaps, and a controllable propeller using our Piper Seminole PA-44-180
  airplane. You can earn your complex endorsement, or combine your
  training to earn your complex endorsement and multi-engine rating.*