Typically ABS effects the front braking system only, though in newer cars this isnt the case, however in systems where rear brakes are involved in the ABS system, i would think that pulling the e brake would have no effect, or just disable the rear portion. However this would only be a guess.
In the OP's defense, this post is asinine, the car cut him off, he was not following the car, it jumped in front of him.
Though I do agree with the general consensus of the thread in that pulling the e brake in a emergency braking situation can only hurt you, not help you. I agree with the poster saying to try and break that habit. The brake pedal, if applied in time in most situations, with a properly inflated set of tires bearing proper tread depth, should stop the car relatively quickly. If your tires and braking system were properly maintained, you would not have needed to pull the brake in these same situations, and honestly, im not sure doing so in your situations helped you at all.