Depends on the fan and how it is powered. Drawing fan power from motherboard/card headers which alter fan speed according to temperature generally results in a noisy PC as the fan speeds are poorly callibrated and the board designers play very safe because they assume, sensibly, that e.g. the cpu cooler will be a standard Intel one with a small fan that requires high speed to push much air and won't reliably start at low voltage.
Switch the cooler for e.g. a huge Noctua heatpipe one and the fan for a much more efficient model that will start at low voltage and the motherboard design assumptions no longer apply.
Stock fans are nearly always noisy to start with. If power for the fan is drawn from the GPU card and changed according to temperature automatically then what you describe might happen. However, the noise is still mostly coming from the motor.
Cleaning the fan won't help if the motor is too noisy to start with or if the blades create noisy turbulence.
Quite a few GPU BIOS can be edited to make the fan much quieter. One I had started with the fan running at a minimum of 70% then ramped it to 100% by the time temperatures reached 45C, less than half the rated temp. for the card. It sounded like a vacuum cleaner. After some tweaking I reduced the fan speed to a maximum of 40% and the card ran quite happily for the 3-4 year lifespan of that PC. Sure, the card ran hotter, but still well within spec.
And if the fans are drawing power from a fan control unit rather than motherboard headers that provide varying voltage then cleaning the blades will help cooling efficiency but not reduce noise because the fan won't have ramped up in the first place.
Anyway, we're probably well off topic for the SonarX forum by now...