choclatechef was on target, as usual.
Ice is +32-F ... adding salt to make it a 20% brine lowers the temp to about +2-F. The coldest a brine solution can get is -2-F (23% brine).
Since the sugar in the mix lowers the water's freezing point ... without the salt you would probably just wind up thick "soup". In other words, the ice cream "won't make".
As for overchurning ... (1) you'll not be able to remove the ice cream from the cannister without great difficulty, (2) you'll burn out the motor as the mixture becomes too thick, and if mixing my hand (3) it will become impossible to turn the crank. At this point you have exceeded the churning phase and moved into the early freezing stage.
I found a site that you might find of some interest ... on the Science of Ice Cream: http://www.foodsci.uoguelph.ca/dairyedu/findsci.html