I'm not sure that TypedArray will help that much. For web apps, most of the data is strings and at some point you have to deserialize the strings so that regular JavaScript code can work with them (rather than asm.js code which would work with the bytes directly).
The proof of concept would be to send an array of strings as bytes in a TypedArray, deserialize it to an array of JavaScript strings using JavaScript (not native code), and show that this is about as fast as doing the same thing using JSON.parse(). It seems likely that JSON.parse() will have an easier time creating all those JavaScript strings and other objects at once from native code.
The proof of concept would be to send an array of strings as bytes in a TypedArray, deserialize it to an array of JavaScript strings using JavaScript (not native code), and show that this is about as fast as doing the same thing using JSON.parse(). It seems likely that JSON.parse() will have an easier time creating all those JavaScript strings and other objects at once from native code.