No, leaving your air conditioner on recirculate mode does not save gas. The recirculate mode in an air conditioner simply recirculates the air inside the vehicle rather than drawing in fresh air from outside. It is primarily designed to maintain the interior temperature and reduce the amount of hot or cold air from outside that enters the cabin.
The air conditioner in a vehicle does not directly use gasoline as a fuel source. It operates using the vehicle's electrical system, which is powered by the engine and the vehicle's battery. So, the fuel efficiency of your vehicle is not affected by whether you have the air conditioner on recirculate mode or not.
However, it's worth noting that running the air conditioner in general can have a small impact on fuel efficiency. The air conditioner places an additional load on the engine, which requires more fuel to maintain the same level of power. So, if you're concerned about saving gas, it's advisable to use the air conditioner sparingly or at lower settings when possible.