I've seen a few examples of people getting other qualifications in the Australian context:
- Some universities require or encourage lecturers to get a qualification (perhaps a diploma) related to higher education teaching. These courses are often provided by the employing university.
- Some academics want to expand their skill set; doing a formal qualification is one way of doing this. It really depends on circumstances and personal goals. Often an academic has a choice between self-study or doing a formal qualification.
In general life, many people do a degree part-time while they work full-time. If you are still able to perform your duties at your job, then there typically wont be any issue with the study.
Of course, if you need some time off from your job to attend classes, then in most jobs you would typically want the support of your supervisor.
In an academic context, if the study is related to your research or teaching, then a supervisor (e.g., a Head of Department) is likely to give such support. Furthermore, most academics have a high degree of autonomy in how they spend their time, such that no one is keeping track of when they go off campus, whether that be to attend a colloquium, collaborate with other researchers, or do a little study somewhere else.