You can set the background to black already and see if it changes. In fact this was written:

"We also measured how the content displayed on the
LCD affected its power consumption: 33.1 mW for a
completely white screen, and 74.2 mW for a a black
screen. Display content can therefore affect overall
power consumption by up to 43 mW"
http://www.nicta.com.au/pub-download/full/3587/

As such your claim is false for the model given in the paper. Don't fall for those wallpaper sites and they are a fine source of smart phone malware.
Bob