Thanks for the response. Unfortunately I can't say that I had the same experience. I had an Icon for well over a year paired to my iPhone 4 and A2DP was activated on it. The only problem I ever ran into was that occasionally my music would start playing through it if I plugged it into my car docking cable (which would start the iPod playback). But, as I understood it that was partially what the A2DP protocol was faciliating.
Other than that, had no problems hearing notifications of any kind, with A2DP enabled while my headset was on and paired. Those tones never played through my headset. Phone would ring, and in my headset I would hear "call from - - - - - "
I didn't comment before that I tried to solve this by turning OFF A2DP. It does fix the issue with notifications playing through my headset – however it created a whole new problem, where if I voice-dial from my headset, I can no longer hear the audio from the iPhone through the headset even though the headset is the current audio output. I have to switch it on and off again, and then dial through my phone. It's extremely frustrating, but since it's worse to not hear people talking then the actual ringtone, I've re-enabled A2DP, and just shut the headset off.
Kind of ridiculous for a $80 piece of electronics.