The formula for dissipated power
$$ P = \frac{V^2}{R} $$
is valid only for purely resistive elements, like straight piece of wire or a resistor. It is not valid for elements that manifest strong EM induction effects, like coil or a fan where there is an electromotor with coils of wire inside.
This is because the Ohm's law of proportionality of current to voltage
$$ I = V/R $$
is not valid for AC current in a coil. One must account for the self-induced emf force in the coil which decreases the current; the faster the fan spins, the greater the decreasing effect.
A general result of EM induction on the coil is that large current may flow in the wires, but it dissipates much less energy than DC current would.
The answer to your question is that the faster the fan, the greater the transfer of energy from EM energy into air flow energy, but also the higher the impedance of the motor, so it is not so easy to say whether the fan draws more or less. It would require more detailed analysis, taking into account the construction of the motor. But if the construction was done as efficient as possible, I think the result would almost certainly be : the higher the speed, the greater the power draw.