Yes on the scheduling, public speaking, communicating, time management, business process management and other areas that most people do or should do at some point in their job. Accounting isn't in this list as not everyone is into finance and understanding that domain.
It makes one a better programmer in having to deal with people which I'd guess 99% of time is true. How do I get the requirements out of another person? What design considerations should I know? Can I present my implemented solution for testing in an easy manner? All these require the ability to communicate in both asking questions and giving answers as there may be questions for me in this process as well.
People who manage programmers should be required to take some classes on software development methodology, yes, but programming in general, no. The difference may appear subtle but the idea is that I'd expect the manager to know what the main steps are in my work at a high level, not necessarily how to code up FizzBuzz. The scale and complexity can also be a factor as sometimes when coding on big systems, it isn't easy to give an introductory course on that material. Examples would be ERP or CRM system that I'm not sure I'd want to picture the curriculum to cover that in a Programming 101 course.