Jack Daniels (the company) confirmed that this is more than likely. Unfortunately, there is little to no documentation on the major impact slaves had on the American whiskey/ distillation industry. See an article about this in the New York Times.
People were taken from Ireland and made slaves. People were taken from their Indian Tribes and made slaves. People were taken from China and made slaves. People were taken from Germany and made slaves.
Note the clothing in the photo on the right, this is still the story of America. A man was lynched this year. This is not history, but the continuation of systematic violence used to instill fear and control people of color.