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.
This means compiling the lib to wasm, right? At first I was thinking of running JS clientside that imports some C lib somehow, which confused me.