Difficulty number 1:
One type of GPS may be direct conversion (that's not regenerative, by the way - it's sometimes called 'zero IF') and not radiate and another may. especially if we start talking about cheap imports from the far east, where despite all the so called rules, compliance with EU and other standards may well be imaginary. So you DON'T know, except by experiment, and when you add up all the possibilities in a modern airliner, with all the variations of stuff pax are carrying, the possibilities of interference multiply very quickly. In fact, if you have N signals, the simplest combination (3rd order distortion for the techies) gives 2N(N-1) possible interfering signals.
Difficulty number 2:
Aircraft cabling does degrade over the years, and it's a well known phenomena. It's not always possible to determine by visual inspection if the shielding is complete, or that there's no corrosion, and complete rewiring every year just would be too expensive.I seem to remember an article in IEEE Spectrum a few years ago in which they said something like a 767 has over 70 antennas, and I can well believe it. So there is a fair amount of careful; design goes in in the first place in frequency planning in aircraft installations and so on to minimise the problems, and the introduction of just one extra emission can cause problems.
By the law of Arkwright Sod, it won't happen in every situation. It won't happen every time in the same aircraft. The trouble is that it may only need to happen once. Just as back in the early '60s, some guys in Norway misread the Morse ID of an NDB and flew into the side of a mountain.
Radio systems are always liable to interference. I can readily conceive of easy to make things that could cause chaos around airports and for obvious reasons, I'm not going to say what or how here. A radio link required to be out for no more than 10 seconds a year has a dedicated frequency and hot stand by equipment. But at the end of the day, you can't guarantee a radio link - you can just do your best. It's because of the interference that major UK airports have specialist interference trackers available all the time. But that doesn't mean that you can throw another parameter into the mix and get away with it.
And to re-iterate, cheap imports from the far east frequently do not meet any of the compliance standards even though they are supposed to do so. Some companies just ignore the rules, including one major UK telecomms firm! All too often, CE on a product just means 'chinese export'.