So I can run asm.js compiled Unreal Engine in my browser then run JavaScript inside of it?

We need to go deeper!

No, because V8 has no interpreter (although they are working on one: https://code.google.com/p/v8/issues/detail?id=4280), only JIT, and JIT doesn't run inside asm.js.

asm.js-compiled JavaScript engine has been done already: https://github.com/jterrace/js.js.