I have taken this course, and currently taking up the other courses in the specialization. More advanced FP concepts are touched upon in the second course (but not extensive). I think going through the first two courses should help in getting comfortable with a) Scala, and b) thinking functionally on a high level.
For grokking FP (and the type systems), I think a good approach would be 1) go through the red book, 2) go through learning scalaz or herding cats by eed3si9n, and 3) reinforce it by using it, either on practice or real-world problems. There are other great resources and communities out there, but this is the strategy I'd go for (especially #3).