Is framing with screws legal?
According to Table R602.3(1) of the International residential code (IRC), you have to use two 16d (3 1/2" x 0.135") fasteners to end nail the top or sole plate to a stud. If the studs were toe nailed to the sole plate, then either three 8d (2 1/2" x 0.133") or two 16d (3 1/2" x 0.135") fasteners would be required.


  International Residential Code 2012
  
  Chapter 6 Wall Construction
  
  Section R602 Wood Wall Framing
  
  R602.3 Design and construction. Exterior walls of wood-frame construction shall be designed and constructed in accordance with the provisions of this chapter and Figures R602.3(1) and R602.3(2) or in accordance with AF&amp;PA’s NDS. Components of exterior walls shall be fastened in accordance with Tables R602.3(1) through R602.3(4)...
  
  


If by some chance these screws are equivalent to 16d nails, then they should be acceptable. However, I doubt they're equivalent, and therefore should not be used.

There's no specific fastener schedule for interior nonbearing walls, while interior load-bearing walls are required to be framed the same as exterior walls.


  R602.4 Interior load-bearing walls. 
  Interior load-bearing walls shall be constructed, framed and fireblocked as specified for exterior walls.
  
  R602.5 Interior nonbearing walls. 
  Interior nonbearing walls shall be permitted to be constructed with 2 inch by 3 inch (51 mm by 76 mm) studs spaced 24 inches (610 mm) on center or, when not part of a braced wall line, 2 inch by 4 inch (51 mm by 102 mm) flat studs spaced at 16 inches (406 mm) on center. Interior nonbearing walls shall be capped with at least a single top plate. Interior nonbearing walls shall be fireblocked in accordance with Section R602.8.