I tried it now in the 747 classic, a simple Garmin GPS (not for aviation use) worked on the ramp, when placed at the right hand rearmost window, aft/lower corner. I only tried on the ramp with window heat off - don't know (yet) if it works with window heat on.
Electronic equipment, especially when they contain transmitters/receivers, yes, that's a good one. On a few occasions gadgets have been either proven or accused of influencing items like flight controls, instrument indications, communication etc. To make it simple, these items are forbidden or some of them only allowed typically when the seat belt sign is off. "All electronic devices", does that include my wristwatch? Off course not - so there is a borderline somewhere!
A GPS approved for use in aircraft is not likely to disturb, especielly as it only contains a receiver (and not a transmitter), however, it still emits a weak signal from the receiver circuit, and if you are told to switch it off, your should of course do so, whether or not you think it disturbs anything.
For older aircraft navigating on an INS, a GPS is highly unlikely to influence anything.