Does operating a fan in lower speed reduce electricity consumption?

Yes. But the consumption of electricity for a fan itself is very less. So the saving will not be very appreciable. There will be a little difference.

The speed of a fan is controlled by a regulator. Earlier we had electrical type of regulators but now a days the regulators are mostly electronic types.

The electrical regulators were cheaper and speed regulation was done through resistors which were decreasing the voltage going to the fan thereby reducing its speed. So the consumption of electricity was less in the fan but there was consumption in the resistor and in nutshell there was no appreciable savings of electricity in reducing the speed.

In electronic type of the regulators the consumption in the regulator is minimal and using them definitely saves the electrical energy in reduced speed mode of a fan. In fact there is an significant saving of about 30-40% from full speed to minimum speed. In some old buildings where old type of electrical regulators are fitted it is advisable to replace them with the electronic regulators for saving the valuable electrical energy.

Earlier there were electrical type of regulators and there was provision of adjustment of the speed with the resistor. Keeping the resistor at slot 1 would allow the fan to move slowly and the remaining energy consumed in the form of electrical energy got wasted and hence there was no saving of power in terms of electrical energy. Energy consumption was not dependant upon with the changing of resistors.
In the existing electronic type of regulator, the pattern of consumption of energy depends upon the speed of the fan. More the speed, more is the power consumption and hence the lesser speed would amount to lesser consumption of electricity. Hence the replacement of the electronic meter would be a wise step in respect of saving power thereby saving money.
In this context, we know that power consumption of a fan per hour is 60 w and considering its operation for around 18 hours. Actual consumption would 1080 w being approx 1 unit of power and hence the bill - payment in respect of energy drawn by the fan is not enormous.