The wiring changes needed to perform this would be a bit of a challenge, and unless you are well versed in the dark arts of bike electrics, then trying to do it is fraught with danger.
The STs dont run hot, so having the fan come on to cool the radiator (thats all it would achieve) would be a waste of time and effort. Something else to consider, is the drain on the battery, as its a small battery you dont want it drained and be unable to restart when you most need it.