Will closing some hvac vents cause blower motor to use more electricity?
A centrifugal blower pushes air.  The more air it pushes, the more power the blower consumes and the slower the blower will run. When you close vents, you are creating a back pressure which reduces the blower's ability to push air. Since the amount of air pushed is reduced, so is the power the blower consumes. At the same time, the speed of the blower will rise.

An interesting corollary of this is if a centrifugal blower from an HVAC system is allowed to operate in open air, it will often burn out due to the excessive power dissipated in the motor from moving more air than what it was designed to do.