Yes it sounds interesting and could very well be possible. I read through the documentation at
DreamCatcher - RadioNerds and there is even a section describing how to set it up to listen to FM radio broadcasts.
The biggest challenge may be finding streaming software to work with it. Most of this linux software receives audio from a sound card. In this case, the audio is in a different digital format coming from the sdr receiver. Others who have experimented with streaming from an sdr using EZStream software have found this problematic, although others seem to have made it work. Myself, I have spent countless hours on it with very little success. When you pipe the audio out from the sdr to the audio processing software and then pipe to a streaming software it uses stdin and stdout. As far as i know only EZStream works with stdin.
If you (or anyone else here) tries out the dreamcatcher, please report back here your experiences, either good or bad.