The modern controlled substances act was passed in 1970, and drug war spending started ramping up through the 1970's, and didn't really get going until the second half of the 1980's: http://blurbrain.com/wp-content/uploads/2013/09/drugs-vs-spe....
So what does the data tell us? Crime started spiking up about 10 years before the drug war even started. The big jump in drug war spending in the 1980's happened after two decades of rising crime, when crime rates were already near their peak. So if anything, the federal drug war (or peoples' appetite to wage it) seems to be a reaction to rising crime, rather than a cause.
Now, you could also say rising crime was the result of prohibition itself, not just the drug war per se. But narcotics began to be heavily regulated and effectively banned in 1915: http://www.druglibrary.org/schaffer/library/studies/cu/cu8.h....
Now, compare crime rate to incarceration rate and the timeline of the drug war: https://upload.wikimedia.org/wikipedia/commons/4/48/U.S._inc.... The incarceration rate is basically flat until 1975. By that time violent crime had increased by over 2.5x. The mind-blowing thing is that our incarceration rate doesn't catch up to our crime rate until after 1995! I.e. even though our incarceration rate quadruples from 1950 to 1995, in that time violent crime more than quadruples.
It's only after the big drop in crime in the late 1990's that our incarceration rate started to become disproportionate to our violent crime rate.