Do graduate students typically finish coursework?
In every program where I have been a student, a TA, or a faculty member, the default expectation has been "Yes."

That being said, individual instructors or departments may have different policies. I have definitely known of places where balancing coursework and research was intended to be a component of the "trial by fire", and failing there was taken as a bad sign. At the same time, most programs I have been in have been fairly generous with extensions and the like.

But yes, if you're taking my course, I'm expecting you to do the coursework. If you're not, you should at the very least let me know and talk to me about it.