Not generally very adventurous no, especially during the day time hours (although you will get an occasional William Schuman symphony or something), but I listen to Jim Svejda's week-night program fairly regularly and he will dip into 20th century works quite often. Off the top of my head I remember hearing Stravinsky's The Flood, Gerald Finzi's clarinet concerto, Schoenberg's Gurrelieder, and many others on his show. He also plays lots of film music from the 20/21st century, and has current composers as guests from time to time (I heard John Corigliano on there not too long ago).Our station here has pretty good programming, and mostly complete works -- even once in a while some of those gargantuan symphonies by you-know-who and you-know-who. But the station is not very adventurous with respect to works of the 20th century and beyond. It's on the web in real time and can be listened to anywhere. http://www.kusc.org/
Then of course there's the Modern Times program that broadcasts from 10pm-12am PST on Saturday nights that exclusively plays 20th and 21st century works.