variable electromagnet

Ya it is a lot but I think its not actually as much as it sounds like. I made a program with a servo and a light detector whatever its called to count the turns and I think ill get it made alright. Ok I was thinking that was my best option but I called SparkFun and the guy was pretty adamant that it wouldn't work and pwm will not do well for this.

This is the motor driver I was looking at SparkFun Monster Moto Shield - DEV-10182 - SparkFun Electronics

And if its doing a lower speed lower pwm does that take less power from the battery to allow it to last longer or is it the same no matter what pulse.

Also since its pulse I think it would be sending the max current that the battery would do for the pulses like lets say 14.8V battery, 4ohm electromagnet, 3.7Amps. It would be sending 3.7A not all moments as opposed to like 14.8V with current reduced somehow to a continuous 2A. Would these get the coil equally as hot? Would they each allow for efficient battery life

Also I know the pwm is like really fast but this wouldn't cause and vibration or non smooth jolts would it? May be pretty unnoticeable but idk

Also just side thought would there be any benefit or cost to dividing the electromagnet into two and putting one in each port or will that not do anything. I guess it would mean a lower voltage battery. Not sure if thats good or not or doesn't matter