More than just temporary caching; It'll write the ARM instructions into the binary, just like if it were a universal binary - For Mac App Store apps and apps using the Installer it'll happen at install time, for others on first launch. This should follow the .app bundle even. But the transpiled instructions might not be as optimised as if the compiler was given the full source code to create the instructions from the AST rather than from a series of x86 instructions, so there's still reason to compile for ARM yourself.
But excellent post you did; I'm doing my course on compilers now myself