Question: In other words, is it possible to create a Google Chrome app and package it as an .exe or .app so that users won't need Chrome to be installed to run it?

I'm working with NWJS at this time (previously known as Node-Webkit) but I'm interested in the bluetooth/usb APIs from Chrome.

Answer: 
The editor [Atom](https://atom.io/) uses this approach. It is distributed as a binary on many platforms, but underneath is using Chromium and io.js.

The cross-platform desktop application shell portion of atom has been broken into its own project: [atom-shell](https://github.com/atom/atom-shell).

In essence, you are distributing a customized version of the Chromium browser with you app.
Generally, you cannot distribute Chrome Apps the way you are asking, no. Sorry.