Generally, no, air conditioners for homes do not draw in fresh air.
If you want fresh air you need an air-to-air heat exchanger. This brings in air from the outside and exhausts air to the outside at the same time, but moves the heat from one air flow to the other. In the winter, the outgoing air gives up its heat to the incoming air, while during the cooling season the incoming air gives up its heat to the outgoing air. You have to make sure to get one that supports both types of exchanges because many only heat the incoming air.