I believe that the songs they play are properly licensed, much like radio stations. I also believe this cost them a stupidly large amount of money.<p>So I believe your question can be rephrased "Will the cut the studios ask for be insufficient to bankrupt grooveshark or other streaming media suppliers?"
Spotify is making the freemium model work in the UK & other parts of Europe. However, Spotify's success is partly due to their extraordinarily high free-to-premium conversion rate (upwards of 20%).