We could hope for smaller bundles and faster load times, yes. But mostly we should be able to get faster "cruising" execution. Scala.js being statically typed, there is a lot of static guarantees that we lose when compiling to JS. JS engines are very good and can "recover" a lot of it through JIT'ing, but it's still 3x slower than Scala/JVM on average (after warmup of both), so clearly we lose something non-negligible. By compiling to wasm, we would lose the JIT, but keep the static types. It is unclear how fast we would manage to be, but I would hope we can get within 2x of the JVM instead of 3x-ish.
There is a lot of misconception on the Internet that "wasm makes everything faster". For example, a lot of people want to "compile JS down to wasm" to make it faster. That's bullshit, because your language does not have static types to begin with, so you lose the JIT and gain nothing in exchange, which means you'll run much slower. But if you compile a statically typed language down to wasm, you should be able to gain some significant speed.