Gas engines don’t run ACs. They generate electrical current through an alternator which charges the cars battery, and some of that current is used to run the AC, which has its own electrical motor.

Are you suggesting a mechanical linkage between the motor (gas or electric) and the AC compressor?

Why do you think there would be an efficiency gain?

In your scenario, you’d need some sort of belt or gear mechanism that transfers rotational energy from the motor to the A/C compressor. You’d also need a continuously variable gear box that can convert the range of RPMs on the motor into the constant RPM required by the A/C compressor. That’s a lot of efficiency losses.

By contrast the use of battery energy in an a compressor is pretty efficient, especially if it’s a DC compressor (no dc-ac inverter losses)