I'm starting a doctorate focusing on artificial intelligence and network security, and have all of my technical classes paid for and organized. The schedule is currently forecasted at 60-ish hours a week of classes, grading, research, and other required activities. I feel this is reasonable.
However, I'd also like to take advantage of the expertise on campus and take piano lessons offered as credited classes by my school. These classes would be taught by the institute as graded classes but would not contribute in any way to my doctorate requirements or employment. They would be fully paid for by my scholarships, along with any other classes I'm taking.
On the plus side, I feel like learning something outside of my doctorate will make me a better rounded student, and music has always given me a safe, healthy outlet for stress and anxiety. And it seems like such a waste to pass up on free lessons from a professional when I'd be paying upwards of $1000 for lessons from a non-professional anyway.
However, I'm worried about attempting this for a couple reasons:
First, I'm worried that my adviser would see these extra hours as a signal that I'm not working to my maximum potential on his project. It's one thing to have hobbies and outlets, it's another to take extraneous classes that could be replaced with required ones.
Secondly, this could be an easy official scapegoat if anything goes wrong with my research. If I get a B in my required classes, it would be easy to say that the five hours a week in this class could have been used to study.
Finally, while the scholarship contract specifically says "all classes" are paid for, I'm worried it would be seen as unethical to ask the computer science department to pay for a class that has nothing to do with my doctorate.