You'll eventually hit a roadblock. It's turtles all the way down. If you translate libraries your program depends on, then you'll hit the OS API. If you manage to translate the OS, you'll have to emulate all the hardware below it.

Technically it's not impossible, I guess someone could create something that translates all I/O operations into something that reads from the browser storage and renders to the screen, but the amount of work would be pretty insane. It's been done for smaller machines already, just look at any of the JavaScript based emulators like JSNES and so on.