I really don't think that there is a control valve or anything that stops the flow when the air is off, so there should be coolant flowing through the heater core whenever the engine is on. What does this fluid leaking on the carpet look, feel, or smell like? When the engine is cool, open the radiator cap, take a whiff, stick a finger in there. If the liquid on the carpet just smells and looks like water it is probably just condensation. After running the A/C for a while and then parking the car, check for a puddle on the ground behind the passenger tire (this is normal and is just condensation). If there is no puddle on the ground, but the carpet is wet instead, there must be something clogging the condensation drain tube or it is broken.