Car leaking coolant

Nope. The fan only turns on when needed. On GM cars that can be as high as 220 degrees. The water in the coolant will boil at 212 degrees but the boiling point increases 3 degrees for every pound of pressure in the cooling system. The standard radiator cap releases pressure over 15 pounds. That means the water won't boil until long after the fan has turned on. If the leak is significant enough, no pressure will build up and the water could boil before the fan turns on.

If a new hose is leaking, either the clamp wasn't tightened enough or whatever it's connected to might be cracked or corroded. Sometimes it's hard to tell exactly what is leaking and the wrong part might get replaced. You should be able to follow the smoke to the source of the leak. When the engine is cold you can use a pressure tester to pump the system up to pressurize it, then look for seeping coolant. If the leak is too small for that method, you can add a small bottle of dye, drive it a few miles, then search with a black light. The dye will show up as a bright yellow stain.

Caradiodoc

DESCRIPTION
An electric coolant fan aids air flow through the radiator. The fan is driven by an electric motor attached to the radiator support. The fan motor is activated by coolant temperature. If the vehicle is equipped with air conditioning, a switch can activate the fan motor when the compressor is operating.

OPERATION
The PCM regulates voltage to the coolant fan relay, which operates the fan when the engine coolant temperature exceeds 106°C (223°F).