By all accounts, no. The "War on Drugs" in America, as we know it today, is generally dated to Richard Nixon's 1971 United Nations speech, and the subsequent implementation of hard-line drug policies. Keep that year in mind and look at this graph of incarceration rates in the US, courtesy of Wikipedia. It is undeniable that a massive spike in incarceration rates co-incided with the War on Drugs. Now, obviously correlation doesn't imply causation, and we could point to other factors such as the decline of American industry, the effect of the post-1973 OPEC embargo on the US economy, and a general increase in financial hardship amongst the American populace as being behind this boom in the American prison population. But most analysts do indeed attribute the prison explosion to the advent of the War on Drugs (additionally, a more controversial position charges that the emergence of a "prison-industrial complex" also contributed to this). If you are interested in a pop-history summary of the issues involved in your question, and are capable of overlooking the highly biased and ideological slant of the author, then I'd recommend Michelle Alexander's The New Jim Crow: Mass Incarceration in the Age of Colourblindness. Her position is one of an activist, but she does piece together her sources very well to clearly outline how the War on Drugs triggered the massive rise of the US prison population.