Yes. I think a major part of any good employee’s job is to contribute to the department’s work and efforts in a way that reflects on the department manager’s skills and abilities. When that happens, the manager often is targeted for promotion.
Helping my boss get promoted might result in my being considered for his or her job. In that sense, I guess you could say I’m interested in my boss’s job.
For companies to grow and improve, the people who work there must grow and improve. Promotion and advancement within the ranks are signs that a company provides opportunities and recognizes the potential of its employees.