Perhaps, but you wouldn't actually want to run a Scala program that way.

To implement C semantics, Emscripten uses a single, large JavaScript typed array as the heap. To the JS garbage collector, this heap is a big, opaque blob. Then your Scala Native program has its own garbage collector operating within its heap. The two garbage collectors are unaware of each other. This is just a vague intuition on my part, but it seems to me that an arrangement involving nested garbage-collected heaps is bound to be suboptimal. Scala.js is much better in this regard, since Scala objects are just JS objects, sharing a garbage-collected, compactable heap with the other JS objects.

Scala.js is not only about making your Scala app run in the browser. It's also (and mainly) about letting you develop in Scala for the Web environment, which includes manipulating the DOM and calling any existing JavaScript library. Scala Native run with Browsix (or compiled to asm.js/WebAssembly for that matter) would not give you that.

So no, it would not make Scala.js redundant.