Yes, you can modify the base settings. But, you may not have to. You don't really plug the ECU into the dyno computer. A good tuner will change the maps according to data collected on the dyno. Gotta have that human interface.
AFAIK, FAST is not a self learning system.
With these aftermarket systems, there's no need to "burn a chip". You simply plug in a laptop and change whatever parameters you want to change. The ECU places it in memory, and keeps it there pretty much forever. It doesn't need continuous power to maintain the memory like a stoock ECU does.