As stated above, C2 is a html5 game engine..
Html5 will allways have to be run in some sort of webbrowser like environment..
If you want to create an app like you say, you should look into creating a native app that can work without a wrapper..
There isn't another answer to your question.
You won't be able to create this app with Construct2..
i see some examples, and made it one on with phonegap (html + js) and work with a cordova plugin.
But i can't add it very well with construct2. So, yes the app can run in background, but im still working in how add this plugin with C2.