OK. Sorry guys, I was wrong a bit, because I did not notice this until today. As we know, under ConnectedDrive menu, there are 2 extra options achieved with media adapter. One is Apps: Facebook, Twitter and Web Radio. Second one is PlugIn where the music with an iTunes interface like resides. When the BMW Connected app (that is installed on your iPhone) is turned off ONLY the Facebook/Twitter/Web Radio gets disconnected. iTunes music stays on no matter what app you are using in that moment. So Apps appear not to have multitasking function, but PlugIn does (I did not check what happens when video clips from iPhone are played).
No, I do not think you need adapter to have "My Remote App" working, but people may need Tech pkg. as a part of the smartphone integration set up.