It will if the DRM is < +2. I.e., a +1/0/-1 shot on the 1-FP column will cause DM - even by units that can cower.
The phrase "(taking the possibility of Cowering into account) " doesn't mean one checks as if the attack cowers. It really only means that if the only DR what can cause a NMC, is a 1,1 - then units that can cower don't inflict DM.
Tips From The Trenches:
ASL Journal 7, page 44.
A 1 FP attack with +1 DRM inflicts DM on a broken unit and is potentially eligible to inflict encirclement. Both rules (A10.62 and A7.7) require “enough FP (taking the possibility of Cowering into account) to possibly inflict at least a NMC.” On such an attack, an Original 3 DR could inflict a NMC. In contrast, a 2 FP attack with a +3 DRM could qualify only if the attacking unit were exempt from Cowering (e.g., Fanatic, Elite British, leader directed, etc.) since an Original 2 DR would Cower.