I have an XPERIA S with the mod'd FM radio app that worked without the headphones plugged in, but it had to be in a VERY good reception area to pick up a station.
The other way, is just get a 3.5mm stereo plug with approx 60cm of cable (aerial) attached and you've got a cool antenna and then just play the radio through the speaker.
The menu has the "Play in Speaker" option already ... so you've already got all the best options.
Walks away and looks for Bluetooth headphones....
Cool. With a metre of cable attached to a 3.5mm stereo plug I can listen to the radio on my Bluetooth headphones
I have the phone in the best reception location and via the magic of Bluetooth I can listen to the radio (and answer calls) approx 6 metres away.
Schumann ....classical music... all very civilized.