If the GPS receiver is a direct conversion type, then the biggest possible cause of interference is to the on board GPS. Not desirable. But if it's a superhet, then we have a potential problem. If it meets FCC (US) requirements on oscillator radiation, it could well have an Intermediate Frequency such that the local oscillator blocks a DME channel. If it meets EU standards, possibly not - but only possibly, depending upon which stanadrds the manufacturer has decided to declare it compliant to.
radeng I don't know much about the technical stuff in detail but are you saying that if I fly along using the panel mounted Garmin 430 (or whatever) and I've also got a handheld on the yoke...you know just to cross check stuff and perhaps do someone with one while the other shows something else...they might interfere with each other?