Is there a known relation between course pass rate and student feedback?
Yes, this has been rigorously probed in a 1998 study called DUET at Duke University. The study is described in chapters of Valen Johnson, Grade Inflation: A Crisis in College Education.

The correlations you describe had been observed for many decades, but they don't do a very good job of probing what's going on. The correlation could arise because teachers' effectiveness is correlated with students' performance, and therefore with grades; because students give higher ratings in return for lenient grading; or because students attribute success to their own efforts, and failure to the professor.

The DUET study got around these issues with a design that used a pretext to get students to fill out two different online evaluations of their teachers. (This was in the early days of the internet.) They gave evaluations both before and after seeing their final grades. The results showed a time-sequence consistent with a cause-and-effect relationship, with students tending to change their evaluations after seeing their grades.

There is other evidence that student evaluations lack validity, including a famous experiment called "Dr. Fox," in which a very energetic and persuasive lecturer gave a great lecture with total nonsense as the content.

Personally, when I'm on a tenure committee or evaluating an adjunct, the only thing I find useful about the evaluations is if the written comments show a pattern of something objective, e.g., lots of comments complaining that the instructor was often absent.