Honestly, for that class it probably doesn't matter much as it's focusing more on functional programming theory than anything complex in terms of application structure or environment. I did it in Eclipse when I took the first iteration of the course, and I didn't really have much trouble. Unless they've added alternate project files, you'd probably have to convert the worksheets and projects to the IDEA format, and that'd be a bit of a hassle.

That said, for general use I really like the Scala support in IDEA. I'd suggest playing around with the free version a bit - as you mention, Play support is only in Ultimate, but the Scala plugin itself works fine in Community. You can get a feel for how IDEA manages projects, handles debugging, that kind of thing.