I put the widget on my home screen and plugged my headphones in test it out. The difference was slight, at least with the song I was listening to, but it was there.
Mono puts out a single signal. You're hearing the exact same thing through both sides of your headphones. Therefore, it doesn't matter if you have both in or only one, you'd be hearing the same thing. However, stereo puts out two independent signals. You are not hearing the same thing through both sides. It makes the sound "richer".
As I've been writing this, another song came on that had a significant orchestral background. I flipped the mono off and on with the widget, and the different was quite pronounced, so at least on my phone, with the headphones that came with the phone, it's working.