It is quite possible but the decoding unit will have to be capable of the same. Most stations are broadcasting their identity using the same, but it is only restricted to that.
Theoretically, you could modulate a text message over the radio signals and have them demodulated with the receiving unit easily. The reason it is not prominently seen is because of the massive diversity of the receiving units, so the stations would not want to loose out on devices not capable of text decription.
In FM Radio setups, the primary channel is used for audio signal while the secondary channel on the same frequency can be used for data carriate too.