I have never come across any substantiated evidence of GSM phones, or any other electronic gadget for that matter, interfering with any navigation avionics in any aircraft.
That said, I wouldn't fly an autopilot-coupled ILS in IMC with my phone (GSM or satellite one) switched on. I know for a fact that my autopilot is sensitive to ground based EM radiation sources.
The interference one can hear in the headset is picked up by the electronics inside ANR headsets,
AFAIK.