No, the primary optimization asm.js brings (at least in OdinMonkey) is AOT compilation.
Fully typed code should produce the same code from IonMonkey without OdinMonkey: the problem is you have to get up to 10k calls (at least last I looked!) of a function before you get there; but once you are there it is just as good. It's the build-up, through the interpreter and the less efficient code-generators (in terms of code generated, that is; they're more efficient in terms of their own runtime), which really hurts.