The engine would have to be rewritten from the ground up, including plugs. In a different language.
It's basically the same as asking for a native export.
I read up on the subject a bit.
tinyurl.com/jy5dr2c
Seems like WebAssembly (webasm) is meant to allow C/C++ to be compiled to run in a web browser.
Newt, you are correct, it would be like asking for a native exporter level of support. That is why Unity and Godot (and other game engine) are relying on webasm: to have a relatively easy port of their native exporters!
It would be sour cherries for Scrirra to swallow when it turns out that competing game engines' native exporters ported to WebAssembly perform better than hand-written native asm javascript and canvas in the browsers.
A static language converted to webasm executes faster than javascript converted to webasm. That is saying that Construct 3's javascript is converted to webasm in the first place, which is not the case, right?
And since javascript (asm) is JIT compiled (meaning it must be parsed, typechecked, interpreted and finally compiled) it will be slower than webasm, which is parsed and then compiled. According to the linked article a 5% speedup is already the case, with future speedups expected.
The conclusion is that competing game engines will (probably) offer better performing web games with improved predictability because they have native exporters in the first place which are ported to webasm. Isn't that ironic?
Of course, in practice it will probably not make much of a difference for most games, going by what Ashley says in his article. I do suspect that it may matter for lower spec'd hardware.