Now am I thinking right, or does the air have to be saturated, ie water droplets be present for the ice to actually buiild up?
Water droplets have to be present for ice to build up. Because of the cooling in the carb, unsaturated ambient air can become saturated and cause icing.
However, the cases we're comparing are:
1) Take air at a particular temperature and humidity and cool it by 30 degC in the carb. (carb heat off)
2) Take air at the same temperature and humidity, heat it by (say) 20 degC and then cool it by 30 degC in the carb. (partial carb heat)
The amount of water available in the carb as supercooled droplets to cause icing is the same in each case (or in fact, rather more in case 1),
unless there are ice crystals in the starting sample of air.