Whether you can get GPS data from a GPS mouse depends on the particular device you select. The frequency that it generates data will also depend on the particular device.
The one device I looked at had a much higher price, and much larger size, than a GPS on a shield. If it were me doing this, I'd get a shield with GPS, and know that I would be able to communicate with it.
The accuracy of a GPS is typically +/- 3 meters. 20 unique samples per second would have the robot moving 60 meters per second.
A xbee could transmit the GPS data at that speed, if the GPS can. But, transmit it where?
One hour of data at 20 samples per second is going to be about 6 Meg of data. Even a small SD card will hold that much.