I don't believe that this is possible, as a standard/recommendation, due to the separation of signaling from media circuits. The process of answering a call is separated from the interconnection of the circuits, and the latter is only possible/feasible after the call-status of acknowledgement of an answered call is returned.
The ringing heard on the caller side isn't necessarily indicative of the call-progress as it can and is often first provided by the originating network (you've heard double ringing before?), and the custom ringtones/messages are from a in-network peripheral that the called device is unattached from other than by account configuration stored separately from the physical device.
However, as a customization, this is not really a challenge for a non-standard device to capture the audio from the microphone of the pre-ringing device and send it back through the network as SMS content.