The thing about GPS is true....it shouldn't be a problem. jollyrog I assume that your Garmin is designed for use in aircraft (do they even makes ones that aren't?) and you've probably used it hundreds of times in the air before.
I don't know whether the fact that it probably wasn't IFR certified has anything to do with this?
Mobile phones are a completely different issue though, I have on several occasions left my phone on in the cockpit by accident and heard that sound in the headphones when someone is ringing it. Interference with the autopilot and the ILS has apparently been reported in the past as well that was thought to come from mobile phones.