I think there is one thing we need to keep in mind for the Romans (not that you mentioned them but others have). To my (limited) knowledge theough most of its history members of the Roman army were to pay for their armor, tents, clothes, weapons, food, medical treatment, funerals... While perhaps making it back in war booty or by getting the honor of settling in some backwater surrounded by angry locals after a decade of forced service. Who will pay for this? If it is rare, then it is likely to be kept by those with deep purses, perhaps being used as a hangover cure or by tradesmen needing to wake earlier. For the military people are not going to be able to march a couple extra hours just because they got stimulants that helped in the morning. They still need sleep. Might be useful for watchmen, though. I also think bakers would be the main users of the drink, if the prices were reasonable.