An LCD panel in of itself doesn't draw much current and a driver transistor to manage the backlight is a simple thing to do.
For that matter You Could just use a PNP transistor from a digital pin on the Arduino to turn off power to the whole LCD panel...
Rather than trying to control the contrast with the Arduino and save yourself a lot of code grief...
For that matter the Arduino Could be the VCC for the contrast pin... or you could simply "Gate" the contrast off with a transistor.
As I remember If you pull the pin about 2 - 3V high it will turn off the LCD contrast as that pin wants to be about .5 to 1V positive and any higher voltage will blank the display...
All are easy things to do and much easier than trying to PWM the contrast pin.
Although your idea is certainly do-able it is a whole lot more complication than is required... IMO
The methods I mentioned would be my first choice and PWM control of the device would be a method I would study real hard to avoid as it is too much code for too little a problem.
Occams Razor is a useful philosophy, I have found... mostly the hard way thus my tag line.
Here is a good reference from Wikihttp://en.wikipedia.org/wiki/Occam's_razor. Try reading it and see if you can't simplify things...
Fewer things to go wrong in the end, Most likely.
Doc