this will work if you are listening to songs or videos saved on your device or memory card. you won't be able to stream as this option turns your radio off meaning you are not connected to the network. you won't receive any data, calls until you restore your connections.
is this what you are looking to do? if you could expand a little more...
you can try turning your notifications to silent. i've found that the media player still pauses when a message comes in.
EDIT: i just turned my notification to silent and sent an email and the MP3 player did not pause! have to test on other messages. i thought that i tried this before and it didn't work.
so..make a profile for music or use the quiet one and see if that works for you!