It's funny you bring this up because today when I got back to the office today from lunch I was in a hurry to get out of the car and forgot to put it in park when I pushed the start/stop button. The car and A/C turned off because I was stopped but the radio stayed on. I thought that was strange but relized right away I still had the car in drive. I put the car in park took my foot off the brake and had to push the start/stop button two more times to turn the car completely off. So I guess you can turn the car off and leave the radio on, but I don't think this method is good for the car.
Oh and the reason I was in a hurry is because a cute girl from the office was walking out to her car and I wanted to talk to her