For those who use atemi, is uke allowed to do a technique off of your strike?
Do you ever practice counters in this manner, or is it only a training device?
The way we practice katamenuchi is one way that we practice this. After uke grabs the shoulder we go to strike uke in the face and the uke blocks the strike. When done correctly it happens in pretty quick succession and looks like uke is grabbing the shoulder and hitting the face at the same time. This is one of our test techniques for 1st kyu and up. I watched one winter camp where Yamada Sensei corrected everyone testing for doing it the second way and that they should be doing it the first, and Sunday morning's class was techniques from Katamenuchi.
I have also trained when people come around with a second strike or punch.