Dylan of Household Hacker put this life hack to the test. As the video above shows, the dry towel does reduce the moisture in the wet clothing. However, as Dylan points out, you have to take the towel out of the dryer after, say, 15 minutes for this to be effective. Otherwise, that towel is still contributing to the moisture in the dryer and even extending the drying time.
So, in short, put a dry towel in the dryer with your wet clothes for faster drying time, but take it out 15-20 minutes afterwards.
Will a towel make my clothes dry faster? [YouTube]