No, because that would disrupt the breathing pattern. Most exercises in the basic routine of kundalini yoga are based on the bhastrika (breath of fire). If you start chanting, you can't do the bhastrika properly. This applies to the first six kriyas of the routine. I guess there's no harm in chanting it after each of the first five kriyas, during the rest period.
Furthermore, Sat Nam is not chanted in the second kriya, it is thought. It is only said in the last kriya.