Yeah, though I haven't worked on that directly, I'm sure it's not trivial, but I think there is sufficient demand. Check out http://pypyjs.org , which uses emscripten to compile to asm.js and then bolts on a custom JIT that emits asm.js, for one example of a project that is already trying something like this.
It is not a walk in the park to compile runtime into WebAssembly (unless you are just compiling an interpreter).
Performant runtimes usually include machine specific backends and/or hand written assembly code. You'll need to port that all to target WASM too.