Google Music has partnered with in.com, saavn and saregama to deliver this.
My attempt to search for any Tamil Songs returned very few albums which are very old as you can see. Probably Google will add it in future.
Apart from this, I noticed that hearing songs from this portal was very user friendly, loads quickly from net and no irritating ads at the start of the songs. Hope Google doesn’t add it in the future!
You can try hearing to it at http://www.google.co.in/music