The idea gets my vote!
(Shoutcast is the one I've been listening to but now that I'm aware of it I'll give Icecast a listen.)Perhaps it could be an option melded into the Immersive Sounds "amience" mod. Version 0.31 of "ambience" allows seperate, in-game, control of sounds and music... why not add a third option of webradio?
Now some may chime in with a more pragmatic solution: just play the webradio through your media player while you are playing Minetest. To wit I would reply, "Many creative endevours are pursued not because they are practical but because they can be done."
Of more technical concern, running a full-featured media player along side Minetest is a strain on system resources (espicially if your computer is more than a couple years old). Isn't one of Minetest's much touted strengths is that it can run decently enough on older hardware?
Maybe integrating an existing command-line player could be done? Here's a web article on Linux.com,
"CLI audio players for Linux":
http://archive09.linux.com/feature/124907