If you just want to run some computational code (which is the case for most of the Wasm use today), it will Just Work, as you say.
In fact, that is how I sped up a webpage: I just wrote myself the minimal support needed to run the code that computed X, and that's it. I don't want the entire world or standard library for computational bits to work.
The example I pointed out was for extra stuff, sure, but even just to get a compiler to spit things out, work needs to be done. I don't know Ada's compiler well enough to point to where that work is, but here's the initial implementation of the asmjs and wasm targets in rustc, for example https://github.com/rust-lang/rust/pull/36339
This is just true of any architecture. LLVM is a toolkit, it isn't magic.
If you just want to run some computational code (which is the case for most of the Wasm use today), it will Just Work, as you say.
In fact, that is how I sped up a webpage: I just wrote myself the minimal support needed to run the code that computed X, and that's it. I don't want the entire world or standard library for computational bits to work.