Water cooling isn't really to help emissions - it's to keep noise levels down. A cylinder head and barrel is quieter if it's covered by a water jacket instead of a thinner barrel and cooling fins.
Having owned both liquid and air cooled EFI equipped bikes, I'd argue that water cooling helps control fuel management, and thereby emissions by allowing the ECU to see more consistent engine temperature reading via a coolant temperature sensor, which doesn't fluctuate nearly as much as an AIT sensor.
It also allows the coolant to be routed to known engine hot spots for instance the area between the exhaust valves, which enhances reliability. As an afterthought, liquid cooled engines also maintain a more consistent operating temperature, especially during very hot or very cold conditions.