Assuming you are talking about the area to the "northwest" of the beam then I would say not, the spacing indicated far exceeds 168 square feet.
With a 37" deep beam let's not confuse ourselves by calling it a beam, as far as I am concerned you may as well call it a wall. The heads along the wall are spaced 17' apart (12*1.414 plus a little)
Here is another sketch which may explain the the reasoning of why I think it is still 168 sq ft when you cut an area in half and keep the same head location. Why would one be ok but the other not?
Maybe I'm not visuallsing properly but your spacing looks like it is 155ft2. Depends on exactly what dimension is required for the pink boxes to provide coverage. Where I have placed the wall (estimate) would mean S=13'-10 1/2" (6'-5 1/4"x2) multiplied by 12'-0" (distance between sprinklers 'L')
coarts. I had been guessing with the wall dimensions. Had missed the 7' dimension you have shown on the lower left. Given that, I would agree that your spacing would be 168ft2.
