Not all codes require an air gap at sinktop level.
Yes, but an air gap is good idea for 3 reasons:
1. It protects the dishwashers from sewage back-flow and contamination
in the drain line

2. It introduces air to the top most level in order to break the water
flow and to prevent siphoning in the drain line after the drain
period.

3. It gives the water somewhere to go if there is a blockage at the
disposer, which helps protect the dishwasher pump.