Do basement walls with metal framing and foam insulation require fireblocking and draftstopping?
The foam insulation itself is combustible, hence the requirement for a thermal barrier.

According to the 2012 IRC:


  R316.4 Thermal barrier.
  
  Unless otherwise allowed in Section R316.5 or Section R316.6, foam plastic shall be separated from the interior of a building by an approved thermal barrier of minimum 1/2 inch (12.7 mm) gypsum wallboard or a material that is tested in accordance with and meets the acceptance criteria of both the Temperature Transmission Fire Test and the Integrity Fire Test of NFPA 275.


I also want to add that not only is foam plastic combustible, it is dangerously so. Many of the most deadly building fires in recent history have involved improperly-protected foam insulation or accoustic material. E.g. the 2003 Station Fire in RI and the 2013 Kiss nightclub fire in Brazil. Obviously the stakes are a little lower in a private residence, but do not make the mistake of thinking plastic is noncombustible.