It's implementation dependent. Most implementations JIT Wasm up front (I think Chakra is the only engine that interprets). So, JS loads faster because almost all engines interpret first (all?).
Chakra uses a pure JIT approach? I thought they interpret both in JS and Wasm?
"WebKit’s WebAssembly implementation, like our JavaScript implementation, uses a tiering system to balance startup costs with throughput. Currently, there are two tiers to the engine: the Build Bytecode Quickly (BBQ) tier and the Optimized Machine-code Generator (OMG) tier. Both rely on the B3 JIT as their low-level optimizer."
Consider also this is perhaps a false distinction. V8 always produces machine code when running JS IIRC. And that code is JITed doesn't mean the entire module is.
They used to. They stopped doing that because it made initial load too slow...