The manager is a kind of teacher. who agrees?

I definitely agree with the definition that you gave. I would also add one more verb: trust, the manager should trust that the students are free.... 

I read a book which suggested that to be a good teacher you have to fulfill for main needs for your students that is (1) the need to feel that they are powerful; the need to feel they are free; the need to feel that they are a part of a group and the need to have fun. I believe this also what a good manager should do. Therefore, in answering your question, yes I totally agree.