You can import C (and many others) libraries without re-implementing it in JS for browsers. In my company's case, we compile C-written libopus almost directly to encode audio streams into Opus on browsers, not on servers. In this way we benefit much less data traffic and server CPU loads.
Yes. The C lib will be compiled into wasm. You can use the wasm-compiled code in a browser through JS wrappers. So you can say importing C lib on JS client side anyway.
Note that wasm's main objective is to run non-JS code on browsers, not for a faster JS.