How is it possible to feed the output signal back to input using a TRRS connector
Yes. But, I would get something cheaper.

Search for TRRS splitters. It splits a TRRS connector to a mic and a headphone connector.

Like this one:


http://www.amazon.com/Headset-Buddy-Smartphone-Computer-Blackberry/dp/B002SK66OY/

That said, here are at least two issues I can think of:


Headphone output levels are typically higher than what a mic input expects. To start off, I would test on a device that is not your most expensive device. You should also start off with a low volume and work up from there. You can also avoid clipping by attenuating the signal before you loop it back in.
What happens to the signal depends on how an app is using the mic input. Of course this is in your control if you are writing the app. But something to think about.