My experience with Karate folks is that...it depends. It depends upon which style, and who the instructor is. Shotokan seems less likely to have those round punches - they really like those angles. I think almost any school would have something about mixing up the footwork and punches to different rhythms, rather than just the punch-step drills that are in the kata.Besides jab and cross, does Karate have hook, uppercut, and overhand? Also does the concept of "1 step multiple punches" exist in Karate?
IMO, some TMA striking skill are just too linear without 3 dimensional striking. If one always trains 2 dimensional linear punches, he may not feel comfortable to deal with 3 dimensional punches such as jab/cross, hook, uppercut, overhand.