JS will not compile to WASM.
But yes, that's the future I'd like to see. Browsers only have a WASM engine, and provide a JS->WASM compiler client-side for backwards compatibility.
You'll need most of a runtime anyway, since it provides much more than GC.
Obviously if we're trying to run a full JVM or CLR in WebAssembly, that will cause problems, but C# and F# both have compile-to-js targets that would likely just get faster.