Even if you use language X that compiles to javascript ,you still need to learn javascript, Or it's a bit like learning rails without understanding ruby.
Sure for special cases knowing those things can help get the very best out of your code, but for the other 99% of the time, it is not necessary.
(Edit: Not that I recommend Dart over JS necessarily, but I don't agree with your argument.)
But you DO need to learn Javascript to use Dart on web apps, so the comparison is irrelevant.
For things like CoffeeScript, which are fairly thin layers over another language, I'd always advise to just learn JS first. Dart and Clojurescript though are so far removed from their compilation target that you don't really need to know the JS, as long as there's good library support for what you want to do. In the case of clojurescript the interop is so seamless that it puts the focus on learning the APIs, which is where the true complexity lies. Of course, and even more so with typing, you also have the compiler to back you up.
It really compiles, so you don't have to worry about it. The languages are so similar that stuff that is fast in Dartium will work pretty fine in JS.