Why would a GPS need a mechanical sender for speed? A GPS have the ability to automatically calculate the speed based on the time to receive the signal from a specific sallelite, then calculate the difference is time to receive a signal a few seconds later. Then the GPS calculates the difference in time bwteen the two signals and determines how far you've travelled. This is done with the position of the satellite being in geosynchronous orbit. If you have a GPS in your car, then this also has this capability. This is how it estimates time to arrival. You don't drag a wheel behind you in the car.
The paddle is definitely for a speedometer, but I seriously doubt it's for the GPS. I would suspect this was part of a fish finder package or is connected to the primary speedo,.