No Wifi needed. and you are right, the SuperCap will store some GPS data for a few hours.
This would mean, if you have a GPS fix (led blinking) and power off the device and move it outside of Wifi range (or shut wifi down). when you power up the BerryGPS, it should only take a minute or two to get a GPS fix again (as long as it is within a few kilometers from where it last had a fix).
The device would even get a GPS fix if you powered only with a 3.3v power supply. no need for a microcontroller.
Are you testing outside with clear access to sky?
Peter --OzzMaker.com --